CN111342450B - Robust energy management method considering uncertain photovoltaic and load for traction power supply system - Google Patents
Robust energy management method considering uncertain photovoltaic and load for traction power supply system Download PDFInfo
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Abstract
The invention discloses a robust energy management method for a traction power supply system considering uncertain photovoltaic and load, which comprises the following steps of: 1. acquiring photovoltaic output data in a load process of a traction substation, and constructing an uncertain set; 2. establishing an objective function of a robust optimization model; 3. establishing a constraint condition of a robust optimization model, and linearizing the constraint condition of the optimization model; 4. establishing a two-stage robust optimization model according to the objective function obtained in the step (2) and the constraint condition obtained in the step (3); 5. solving the model obtained in the step 4 by using a column and constraint generation algorithm to obtain a traction substation power flow controller, a hybrid energy storage device and a photovoltaic optimal operation plan in the worst scene, namely completing robust energy management of a traction power supply system; the method overcomes the influence of uncertainty of photovoltaic and traction load on the operation of the traction power supply system, improves the operation economy of the traction substation in severe operation environment, and is closer to the reality.
Description
Technical Field
The invention belongs to the field of energy management optimization of a traction power supply system, and particularly relates to a robust energy management method of the traction power supply system considering uncertain photovoltaic and load.
Background
Renewable energy sources in China develop rapidly in recent years, and photovoltaic power generation has the advantages of no pollution, no noise, small regional limitation and the like. Meanwhile, electrified railways represented by high-speed railways and heavy haul railways are constructed and operated in large scale in China, and the operation mileage of high-speed railways in China exceeds 3.5 kilometers by 2019. The electrified railway has the following features: 1) the regional distribution is wide, and the traffic network and the renewable energy network have more geographical intersections, such as Lanzhou New (Wulumangoqi) high-speed rails and Sichuan (Chengdu) Tibetan (Lasa) railways crossing southwest and northwest areas with rich wind and light resources; 2) the traction load is high in demand and has high consumption potential, and particularly, in weak areas of an external power supply, the access of renewable energy sources can also play an important supporting role. Therefore, the photovoltaic-based renewable energy is connected into the traction power supply system to promote local consumption and improve the permeability of the renewable energy.
On the other hand, the electric power department in China charges the electric charges for the electrified railway by adopting two large-scale industrial electricity-consumption power rates, wherein the basic electric charges are charged according to the basic capacity or the maximum demand. Maximum demand charging also sets a "threshold" for minimum installed capacity. From the statistics of railway operation departments, the electricity fee has become one of the main operation payment fees. If the hybrid energy storage system is accessed, the peak clipping and valley filling of the traction load can be effectively realized, the required electric charge and the electric charge are greatly reduced, the regenerative braking energy utilization of a traction power supply system is promoted, and the system operation efficiency is improved. In addition, the requirement of the system on the capacity of the power supply equipment can be reduced. Therefore, the photovoltaic access and hybrid energy storage system in the traction power supply system of the electrified railway are increasingly concerned.
However, the random fluctuating nature of the traction load and the distributed power output, represented by photovoltaic, present challenges to the operation of the traction power supply system. How to effectively deal with uncertain factors in a traction power supply system and realize safe, high-quality and high-efficiency operation is the key for solving the problem of energy management of the traction power supply system.
Disclosure of Invention
In order to overcome the influence of photovoltaic and load uncertainty on a traction power supply system, the electricity charge expenditure cost of a railway department is reduced in the worst scene, and the energy management optimization method is closer to reality. The invention provides a robust energy management method of a traction power supply system considering uncertain photovoltaic and load.
The invention discloses a robust energy management method of a traction power supply system considering uncertain photovoltaic and load, which comprises the following steps:
step 1: acquiring predicted values and fluctuation intervals of traction substation load process data and photovoltaic output data, and constructing uncertain sets of traction load and photovoltaic output;
and 2, step: establishing a target function of a robust optimization model according to the electric charge parameters and the intervals of the load process data and the photovoltaic output data of the traction substation obtained in the step 1;
and step 3: according to power capacity parameters and three-phase voltage unbalance international parameters of a hybrid energy storage system and a photovoltaic system, establishing constraint conditions of a robust optimization model based on the traction substation load process data and the photovoltaic output data interval obtained in the step 1, and linearizing the constraint conditions of the robust optimization model;
and 4, step 4: establishing a robust energy management method of the traction power supply system based on a two-stage robust optimization model according to the objective function obtained in the step 2 and the constraint condition obtained in the step 3;
and 5: and (4) solving the model obtained in the step (4) by using a column and constraint generation algorithm to obtain the optimal charging and discharging power of the hybrid energy storage device, the optimal photovoltaic grid-connected power and the optimal power flow power of a back-to-back converter in the power flow controller under the worst scene, namely completing the robust energy management optimization of the traction power supply system.
Further, in the step 1, the load process data of the traction substation in the existing line can be obtained from the historical load data, and the traction substation in the newly-built line can be obtained by calculating load process simulation software, such as elbase/WEBANET, according to the high-speed railway line, the train and the schedule.
Further, the uncertain set of photovoltaic output and load in step 1 is:
in the formula: p, A and R are the uncertain set of photovoltaic power output, active load and reactive load, p, respectively t 、a t And r t For uncertain variables of photovoltaic contribution, active load and reactive load, Δ p t 、Δa t And Δ r t Respectively represent predicted values p t f 、a t f And r t f Deviation value of (d), parameter Γ p 、Γ a And Γ r Representing uncertainty margin, i.e. the total relative deviation of the uncertainty variable from the predicted value, which ranges from 0 to within a dayTotal time period N T In the meantime.
Further, the objective function in step 2 is:
in the formula: f is an objective function and represents daily operation cost of the traction substation, t is a time period and P is t grid,buy Electric power purchased from the grid for traction substations, P t grid,fed Electric power P fed back to the grid by the traction substation t PV For photovoltaic output, P t b,dis For discharging power of the battery, P t b,ch Charging power for batteries, P t u,dis Discharging power, P, for the super-capacitor t u,ch Charging power to the super capacitor, P t dem In order to demand the amount of power,in order to achieve the cost price of photovoltaic operation and maintenance,in order to keep the cost price of the battery running and maintaining,cost price for operating and maintaining super capacitor, c dem The price of the electricity charge of the required quantity,the price of the electricity purchased by the traction substation is,charge price levied for feedback back to the grid power, N day For the number of days of operation per month,andare all binary variables;
further, the constraint conditions in the step 3 comprise power balance constraint, hybrid energy storage system constraint, public power grid power constraint, photovoltaic power generation constraint, back-to-back converter constraint and three-phase voltage unbalance constraint; the method specifically comprises the following steps:
power balance constraint conditions:
P t grid,buy -P t grid,fed =P t T +P t α (6)
P t α +P t b,dis +P t u,dis +P t PV =P t β +P t b,ch +P t u,ch (7)
P t T +P t β =a t (8)
in the formula: p t T For active power of traction transformers, P t α Is alpha-phase active power, P, of a back-to-back converter t β Is a back-to-back converterActive power of beta phase, Q t β Is beta-phase reactive power, P, of a back-to-back converter t PV The photovoltaic output is obtained;is the maximum limit value of the interaction power between the traction substation and the power grid,is a binary variable representing the power direction of interaction between a traction substation and a power grid,indicating that the interactive power flows from the grid to the traction substation,and the representation interactive power is fed back to the power grid by the traction substation.
Hybrid energy storage system constraint conditions:
in the formula: epsilon b Is the self-discharge rate of the battery, epsilon b Is the self-discharge rate of the super capacitor, eta b,dis Eta, discharge efficiency of the cell b,ch Is the charging efficiency of the battery, eta u,dis Is the discharge efficiency of the super capacitor, eta u,ch To the charging efficiency of the super capacitor, Δ t is the unit time period,for the electric energy stored in the battery during the time period t +1, E t b Storing the electric energy for the battery in the time period t;the electric energy stored by the super capacitor in the time period of t +1,the electric energy stored for the super capacitor in the time period t;is the rated power of the battery and is,the power of the super capacitor is rated,is the minimum state of charge of the battery,the maximum state of charge of the battery is,is the rated capacity of the battery,the capacity of the super capacitor is the rated capacity,the electrical energy stored by the battery for the time period t-1,the electric energy stored by the super capacitor in the t-1 period,the minimum state of charge of the super capacitor is obtained,the maximum charge state of the super capacitor;the electrical energy stored in the battery for the initial period of time each day,the electrical energy stored in the battery for the last period of the day,for the purpose of the initial state of charge per day,the super capacitor stores electric energy for the initial time period every day,the electric energy stored by the super capacitor for the last time period of each day,the initial charge state of the super capacitor every day;andare all binary variables.
Photovoltaic power generation constraint:
0≤P t PV ≤p t (19)
in the formula: p is a radical of t The photovoltaic output uncertain variable is the solar photovoltaic output upper limit value.
Back-to-back converter constraint:
in the formula:the capacity of the alpha phase of the back-to-back converter,the capacity of the beta-phase of the back-to-back converter.
And (3) three-phase voltage unbalance degree constraint:
in the formula: epsilon U For traction substation power grid side three-phase voltage unbalance degree, U S For the grid side line voltage, S cap For the short-circuit capacity of the side line of the power grid,is the upper limit value of the unbalance degree of the three-phase voltage in the national standard,for grid side negative sequence current, U T For the voltage at the outlet of the traction transformer, U α Is the voltage at the alpha-phase outlet of the back-to-back converter, N 1 For single-phase traction transformer transformation ratio, N 2 For high voltage matching transformer transformation ratio, a is complex operator e j120° ,Is the voltage-current phase angle difference of the single-phase traction transformer,is the voltage-current phase angle difference of alpha phases of the back-to-back converter, I T For drawing the transformer current, I α Is the current of the alpha phase of the back-to-back converter.
Further, the constraint condition linearization method in step 3 is as follows:
the max function in equation (5) is linearized by the following equation:
max(P t dem )=P dem,max (25)
in the formula: p is dem,max Is an auxiliary variable representing the maximum demand value during the day.
The formula (21) after linearization is given by:
in the formula: n is a radical of p The number of the sectors is divided into equal parts of a PQ semicircle, and the Q is more than or equal to 0; delta theta is the sector angle (P) k ,Q k ) The coordinates of the division points of the fan shape and the PQ semicircle.
Equation (24) is linearized as follows:
in the formula:andare all auxiliary variables, and are all the auxiliary variables,is a binary variable.
Further, the two-stage robust optimization model for robust energy management of the traction power supply system established in step 4 is as follows:
in the formula: x represents the binary decision variable vector of the first stage,y denotes a second stage continuous decision variable vector, c. b, D, D, E, E, F, F, G, H and I are all parameter matrixes or parameter vectors.
Further, in step 5, based on the robust energy management model of the traction power supply system obtained in step 4, a main model and a sub model of the robust energy management model of the traction power supply system are formed through a column and constraint generation algorithm, and finally the main model and the sub model are solved in an iterative loop manner until a convergence standard is met.
Wherein, the expression of the main model is as follows:
s.t.x∈{0,1} (37)
in the formula: k is the number of iterative solution times, y l The decision variables added to the main model at the first loop,to solve for the worst photovoltaic output obtained by the submodel,for solving the worst active load scenario, r, obtained for the submodel l * And the worst reactive load scene obtained by solving the submodel is shown.
The sub-model expression is:
s.t.By≤d,(γ 1 ) (46)
Dy=e,(γ 2 ) (47)
Fy≤f-Ex * ,(γ 3 ) (48)
Gy≤p,(γ 4 ) (49)
Hy=a,(γ 5 ) (50)
Iy=r,(γ 6 ) (51)
in the formula: x is the number of * Is mainly composed ofModel optimal solution, { gamma { 1 ,γ 2 ,γ 3 ,γ 4 ,γ 5 ,γ 6 Is a dual variable of the constraint.
The submodel equivalent representation method is as follows:
worst scenario p in sub-model * 、a * And r * To not determine the extreme values in sets P, A and R, equations (1) - (3) are therefore equivalent to:
Based on strong dual theory, submodels (45) - (51) are equivalent to:
-B T γ 1 +D T γ 2 -F T γ 3 -G T γ 4 +H T γ 5 +I T γ 6 =c T (56)
γ 1 ≥0,γ 3 ≥0,γ 4 ≥0,γ 2 ,γ 5 ,γ 6 is a free variable (57)
In the formula: lambda, mu, omega 1 And ω 2 Are all auxiliary variables, and are all the auxiliary variables,
the invention has the beneficial effects that:
1. the robust energy management optimization method for the traction power supply system can overcome the influence of uncertainty of photovoltaic and traction load on safe and efficient operation of the traction power supply system, effectively reduces the electric charge expenditure of railway departments, and accords with the development trend of green and intelligent traffic.
2. The robust energy management optimization model of the traction power supply system is established based on the uncertain set of photovoltaic output and traction load, the robustness of the energy management model of the traditional traction power supply system is improved, and the optimality of the traction power supply system in the worst scene is ensured;
3. according to the method, the nonlinear elements in the objective function and the constraint condition are subjected to linearization processing, the mixed integer linear programming model is established, direct solving by using an optimization solver is facilitated, and the complexity of solving the mixed integer nonlinear model is avoided.
Drawings
Fig. 1 is a schematic diagram of a robust energy management structure of a traction power supply system in the invention.
FIG. 2 is a schematic flow chart of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
The structure of a traction power supply system aimed at by the invention is shown in fig. 1, and the flow of the robust energy management method of the traction power supply system considering uncertain photovoltaic and load is shown in fig. 2, specifically:
step 1: based on actual measurement historical data, obtaining predicted values and fluctuation intervals of load process data and photovoltaic output data of the traction substation, and establishing an uncertain set of traction load and photovoltaic output:
in the formula: p, A and R are the uncertain set of photovoltaic power output, active load and reactive load, p, respectively t 、a t And r t For uncertain variables of photovoltaic output, active and reactive loads, Δ p t 、Δa t And Δ r t Respectively represent predicted valuesAnddeviation value of, parameter Γ p 、Γ a And Γ r Representing uncertainty margin, i.e. the total relative deviation of the uncertainty variable from the predicted value, which ranges from 0 to the total time period N of the day T In between.
And 2, step: establishing an objective function of an optimization model according to the electric charge parameters and the intervals of the load process data and the photovoltaic output data of the traction substation obtained in the step 1;
the target function expression is:
in the formula: f is an objective function and represents daily operation cost of the traction substation, t is a time period and P is t grid,buy Electric power purchased from the grid for traction substations, P t grid,fed Electric power P fed back to the grid by the traction substation t PV For photovoltaic output, P t b,dis For discharging power of the battery, P t b,ch Charging power for batteries, P t u,dis Discharging power, P, for the super-capacitor t u,ch Charging power to the super capacitor, P t dem In order to demand the power, the power supply is,in order to achieve the cost price of photovoltaic operation and maintenance,in order to maintain the cost price of the battery operation,cost price for operating and maintaining super capacitor, c dem The price of the required electricity charge is calculated,the price of the electricity purchased by the traction substation is low,charge price levied for feedback back to the grid power, N day For the number of days of operation per month,andare all binary variables;
and 3, step 3: establishing constraint conditions of an optimization model based on the traction substation load process data and the photovoltaic output data interval obtained in the step 1 according to power capacity parameters and three-phase voltage unbalance international parameters of the hybrid energy storage system and the photovoltaic system, and linearizing the constraint conditions of the optimization model;
the constraint conditions comprise power balance constraint, hybrid energy storage system constraint, public power grid power constraint, photovoltaic power generation constraint, back-to-back converter constraint in a power flow controller and three-phase unbalance constraint.
The constraints are as follows:
power balance constraint conditions:
P t grid,buy -P t grid,fed =P t T +P t α (6)
P t α +P t b,dis +P t u,dis +P t PV =P t β +P t b,ch +P t u,ch (7)
P t T +P t β =a t (8)
in the formula: p t T For active power of traction transformers, P t α Is alpha-phase active power, P, of a back-to-back converter t β Is the beta-phase active power of the back-to-back converter,is beta-phase reactive power P of a back-to-back converter t PV The photovoltaic output is obtained;is the maximum limit value of the interaction power between the traction substation and the power grid,is a binary variable representing the direction of power interaction between the traction substation and the grid,indicating that the interactive power flows from the grid to the traction substation,and the representation interactive power is fed back to the power grid by the traction substation.
Hybrid energy storage system constraint conditions:
in the formula: epsilon b Is the self-discharge rate of the battery, epsilon b Is the self-discharge rate of the super capacitor, eta b,dis Is the discharge efficiency of the battery, η b,ch Is the charging efficiency of the battery, eta u,dis Is the discharge efficiency of the super capacitor, eta u,ch To the charging efficiency of the super capacitor, Δ t is the unit time period,for the electrical energy stored by the battery during the time period t +1,storing the electric energy for the battery in the time period t;the electric energy stored by the super capacitor in the time period of t +1,the electric energy stored for the super capacitor in the time period t;the power of the battery is rated for the rated power,the power of the super capacitor is rated,is the minimum state of charge of the battery,the maximum state of charge of the battery is,is the rated capacity of the battery and is,the capacity of the super capacitor is the rated capacity,the electrical energy stored by the battery for the time period t-1,the electric energy stored by the super capacitor in the t-1 period,the minimum state of charge of the super capacitor is obtained,the maximum charge state of the super capacitor;the electrical energy stored in the battery for the initial period of time each day,the electrical energy stored in the battery for the last period of the day,for the purpose of the initial state of charge per day,the electric energy stored by the super capacitor for the initial time period every day,the electric energy stored by the super capacitor for the last time period of each day,the initial charge state of the super capacitor every day;andare all binary variables.
Photovoltaic power generation constraint:
0≤P t PV ≤p t (19)
in the formula: p is a radical of t The photovoltaic output uncertain variable is the solar photovoltaic output upper limit value.
Back-to-back converter constraint:
in the formula:the capacity of the alpha phase of the back-to-back converter,is the capacity of the beta-phase of the back-to-back converter.
And (3) three-phase voltage unbalance degree constraint:
in the formula: epsilon U For traction substation power grid side three-phase voltage unbalance degree, U S For the grid side line voltage, S cap For the short-circuit capacity of the side line of the power grid,is the upper limit value of the unbalance degree of the three-phase voltage in the national standard,for grid side negative sequence current, U T For the voltage at the outlet of the traction transformer, U α Is the voltage at the alpha-phase outlet of the back-to-back converter, N 1 For single-phase traction transformer transformation ratio, N 2 For high voltage matching transformer transformation ratio, a is complex operator e j120° ,Is the voltage-current phase angle difference of the single-phase traction transformer,is the voltage-current phase angle difference of the alpha phase of the back-to-back converter, I T For drawing the transformer current, I α Is the current of the alpha phase of the back-to-back converter.
The constraint linearization method is as follows:
the max function in equation (5) is linearized by the following equation:
max(P t dem )=P dem,max (25)
in the formula: p is dem,max Is an auxiliary variable representing the maximum demand value during the day.
The formula (21) is linearized by the following equation:
in the formula: n is a radical of p The number of the fan-shaped PQ semicircles is equal to that of the fan-shaped PQ semicircles, and the Q is more than or equal to 0; delta theta is the sector angle, (P) k ,Q k ) Is the division point coordinate of the fan shape and the PQ semicircle.
Equation (24) is linearized as follows:
in the formula:andare all auxiliary variables, and are all the auxiliary variables,is a binary variable.
And 4, step 4: establishing a two-stage robust optimization model of robust energy management of the traction power supply system according to the objective function obtained in the step (2) and the constraint condition obtained in the step (3);
the two-stage robust optimization model for robust energy management of the traction power supply system comprises the following steps:
in the formula: x represents the binary decision variable vector of the first stage,y denotes a second stage continuous decision variable vector, c. b, D, D, E, E, F, F, G, H and I are parameter matrixes or parameter vectors.
And 5: and forming a main model and a sub model of the robust energy management model of the traction power supply system through a column and constraint generation algorithm, and finally, circularly and iteratively solving the main model and the sub model by using optimization software (such as a hybrid integer optimization solver CPLEX in a Matlab environment) to obtain the optimal charging and discharging power of the hybrid energy storage device, the optimal photovoltaic grid-connected power and the optimal power flow power of a back-to-back converter in a power flow controller under the worst scene, namely completing the robust energy management optimization of the traction power supply system.
The main model expression is:
s.t.x∈{0,1} (37)
in the formula: k is the number of iterative solution times, y l The decision variables added to the main model at the first loop,to solve for the worst photovoltaic output obtained by the submodel,for solving the worst active load scenario, r, obtained for the submodel l * Representing the worst reactive load scene obtained by solving the submodel;
the sub-model expression is:
s.t.By≤d,(γ 1 ) (46)
Dy=e,(γ 2 ) (47)
Fy≤f-Ex * ,(γ 3 ) (48)
Gy≤p,(γ 4 ) (49)
Hy=a,(γ 5 ) (50)
Iy=r,(γ 6 ) (51)
in the formula: x is the number of * For the optimal solution of the main model, { gamma { 1 ,γ 2 ,γ 3 ,γ 4 ,γ 5 ,γ 6 Is a constraint dual variable;
the submodel equivalent representation method is as follows:
worst scene p in sub-model * 、a * And r * To not determine the extreme values in sets P, A and R, equations (1) - (3) are therefore equivalent to:
based on strong dual theory, submodels (45) - (51) are equivalent to:
-B T γ 1 +D T γ 2 -F T γ 3 -G T γ 4 +H T γ 5 +I T γ 6 =c T (56)
γ 1 ≥0,γ 3 ≥0,γ 4 ≥0,γ 2 ,γ 5 ,γ 6 is a free variable (57)
In the formula: lambda, mu, omega 1 And omega 2 Are all auxiliary variables, and are all the auxiliary variables,
examples
The robust energy management structure of the electrified railway traction power supply system considering uncertain photovoltaic and load is shown in figure 1, the parameters of the energy storage system are shown in table 1, the parameters of a traction substation are shown in table 2, and the power price parameters of a power grid are shown in table 3.
TABLE 1 hybrid energy storage System parameters
TABLE 2 traction substation parameters
TABLE 3 Electricity price parameter
The operating and maintenance costs of other parameters, photovoltaic, battery and super capacitor are all 0.1 rmw/kWh, and the charging c of feedback electric energy fed =-0.8c buy In linearization of PFC converter, the fan angle Δ θ is 30 °, C&The CG algorithm iteration convergence precision epsilon is 0.01. The uncertain interval of the photovoltaic output and the traction load is expressed as [ 1-lambda ] p ,1+λ p ]p f 、[1-λ a ,1+λ a ]a f And [ 1-lambda ] r ,1+λ r ]r f Wherein λ is p 、λ a And λ r For predicting the deviation coefficients, 0.1 is taken.
The robust energy management optimization method of the traction power supply system is compared with the traditional deterministic energy management method, and the results are shown in tables 4 and 5 after simulation calculation.
TABLE 4 comparison of results of deterministic method and robust method under different uncertainty margins
TABLE 5 comparison of deterministic and robust method results under different prediction biases
As can be seen from tables 4 and 5, with the increase of the uncertainty margin and the prediction deviation coefficient, compared with the conventional deterministic energy management method, the robust energy management optimization method for the traction power supply system has the advantages that the total operating cost is lower in the worst scenario, and the saving rate is continuously increased. Particularly, when the prediction deviation coefficient reaches 0.6, the traditional deterministic energy management method has the situation of being unsolvable, so the robustness is low, and the robust energy management optimization method can be solvated in all scenes, so the robustness is high.
The invention provides a double-stage robust model-based energy management robust optimization method for a traction power supply system, which aims at the traction power supply system connected with a photovoltaic power generation system and an energy storage device, takes photovoltaic output and traction load uncertainty into consideration, and provides the double-stage robust model-based energy management robust optimization method for the traction power supply system. According to the method, in the first stage, based on photovoltaic output and traction load prediction information, a charging and discharging strategy of an energy storage device and an electric quantity trading scheme with a power grid are formulated, and in the second stage, the worst scene of the photovoltaic output and traction load and the corresponding optimal power flow are found. The column and constraint generation algorithm is adopted to solve the two-stage robust optimization model, and the result shows that compared with the traditional deterministic energy management method, the robust energy management optimization method has the advantages of optimality and robustness, especially under the condition that the uncertainty of the operating environment is increased. The method makes the energy management method of the traction power supply system more practical and provides a foundation for the access and engineering application of renewable energy sources and energy storage systems in future electrified railways.
Claims (7)
1. The method for managing the robust energy of the traction power supply system in consideration of uncertain photovoltaic and load is characterized by comprising the following steps of:
step 1: acquiring predicted values and fluctuation intervals of traction substation load process data and photovoltaic output data, and constructing uncertain sets of traction load and photovoltaic output;
step 2: establishing a target function of a robust optimization model according to the electric charge parameters and the intervals of the load process data and the photovoltaic output data of the traction substation obtained in the step 1;
and step 3: according to power capacity parameters of a hybrid energy storage system and a photovoltaic system and national standard limit values of three-phase voltage unbalance degrees, establishing constraint conditions of a robust optimization model based on traction substation load process data and photovoltaic output data intervals obtained in the step 1, and linearizing the constraint conditions of the robust optimization model;
and 4, step 4: establishing a robust energy management method of the traction power supply system based on a two-stage robust optimization model according to the objective function obtained in the step 2 and the constraint condition obtained in the step 3;
and 5: and (4) solving the model obtained in the step (4) by using a column and constraint generation algorithm to obtain the optimal charging and discharging power of the hybrid energy storage device, the optimal photovoltaic grid-connected power and the optimal power flow power of a back-to-back converter in the power flow controller under the worst scene, namely completing the robust energy management optimization of the traction power supply system.
2. The method for robust energy management of a traction power supply system considering uncertain photovoltaic and load according to claim 1, wherein the uncertain set of photovoltaic output and load in step 1 is:
in the formula: p, A and R are the uncertain sets of photovoltaic power output, active load and reactive load, p, respectively t 、a t And r t For uncertain variables of photovoltaic output, active and reactive loads, Δ p t 、Δa t And Δ r t Respectively represent predicted valuesAnd r t f Deviation value of, parameter Γ p 、Γ a And Γ r Representing uncertainty margin, i.e. the total relative deviation of the uncertainty variable from the predicted value, which ranges from 0 to the total time period N of the day T In the meantime.
3. The method for robust energy management of a traction power supply system considering uncertain photovoltaic and load according to claim 2, wherein the objective function in the step 2 is as follows:
in the formula: f is an objective function and represents daily operation cost of the traction substation, t is a time period and P is t grid,buy Electric power purchased from the grid for traction substations, P t grid,fed Electric power P fed back to the grid by the traction substation t PV For photovoltaic output, P t b,dis For discharging power of the battery, P t b,ch Charging power for batteries, P t u,dis Discharging power, P, for the super-capacitor t u,ch Charging power to the super capacitor, P t dem In order to demand the amount of power,in order to reduce the cost price of photovoltaic operation and maintenance,in order to maintain the cost price of the battery operation,cost price for operating and maintaining super capacitor, c dem The price of the electricity charge of the required quantity,the price of the electricity purchased by the traction substation is,charge price levied for feedback back to the grid power, N day For the number of days of operation per month,andare all binary variables; p t T For active power of traction transformers, P t α For back-to-back converter alpha-phase active power, P t β Is beta-phase active power of a back-to-back converter,is beta-phase reactive power of a back-to-back converter; p dem,max Is an auxiliary variable representing the maximum demand value during the day;andare all auxiliary variables;
4. the method for robust energy management of a traction power supply system considering uncertain photovoltaic and load according to claim 3, wherein the constraint conditions in the step 3 are as follows:
power balance constraint conditions:
P t grid,buy -P t grid,fed =P t T +P t α (6)
P t α +P t b,dis +P t u,dis +P t PV =P t β +P t b,ch +P t u,ch (7)
P t T +P t β =a t (8)
in the formula: p t T For active power of traction transformers, P t α For back-to-back converter alpha-phase active power, P t β Is the beta-phase active power of the back-to-back converter,is beta-phase reactive power, P, of a back-to-back converter t PV The magnitude of photovoltaic output is obtained;is the maximum limit value of the interaction power between the traction substation and the power grid,is a binary variable representing the power direction of interaction between a traction substation and a power grid,indicating that the interactive power flows from the grid to the traction substation,representing that the interactive power is fed back to the power grid by the traction substation;
hybrid energy storage system constraint conditions:
in the formula: epsilon b Is the self-discharge rate of the battery, epsilon u Is the self-discharge rate of the super capacitor, eta b,dis Is the discharge efficiency of the battery, η b,ch Is the charging efficiency of the battery, eta u,dis Is the discharge efficiency of the super capacitor, eta u,ch To the charging efficiency of the super capacitor, Δ t is the unit time period,for the electrical energy stored by the battery during the time period t +1,storing the electric energy for the battery in the time period t;the electric energy stored by the super capacitor in the time period of t +1,the electric energy stored for the super capacitor in the time period t;is the rated power of the battery and is,the power of the super capacitor is rated, b SOCis the minimum state of charge of the battery,the maximum state of charge of the battery is,is the rated capacity of the battery,the capacity of the super capacitor is rated,the electrical energy stored by the battery for the time period t-1,the electric energy stored by the super capacitor in the period of t-1, u SOCis the minimum state of charge of the super capacitor,the maximum charge state of the super capacitor;the electrical energy stored in the battery for the initial period of the day,the electrical energy stored in the battery for the last period of the day,for the purpose of the initial state of charge per day,the electric energy stored by the super capacitor for the initial time period every day,the stored energy for the super capacitor for the last period of the day,the initial charge state of the super capacitor every day;andare all binary variables;
photovoltaic power generation constraint:
0≤P t PV ≤p t (19)
in the formula: p is a radical of t The photovoltaic output uncertain variable is the solar photovoltaic output upper limit value;
back-to-back converter constraint:
in the formula:the capacity of the alpha phase of the back-to-back converter,the capacity of the beta phase of the back-to-back converter;
and (3) three-phase voltage unbalance degree constraint:
in the formula:ε U for the unbalance of three-phase voltage at the side of the power grid of the traction substation, U S For the grid side line voltage, S cap For the short-circuit capacity on the grid side,is the upper limit value of the unbalance degree of the three-phase voltage in the national standard,for grid side negative sequence current, U T For the voltage at the outlet of the traction transformer, U α Is the voltage at the alpha-phase outlet of the back-to-back converter, N 1 For single-phase traction transformer transformation ratio, N 2 For high voltage matching transformer transformation ratio, a is complex operator e j120° ,Is the voltage-current phase angle difference of the single-phase traction transformer,is the voltage-current phase angle difference of the alpha phase of the back-to-back converter, I T For drawing transformer currents, I α Is the current of the alpha phase of the back-to-back converter.
5. The method for robust energy management of a traction power supply system considering uncertain photovoltaic and load according to claim 4, wherein the constraint condition linearization method in the step 3 is as follows:
the max function in equation (5) is linearized by the following equation:
max(P t dem )=P dem,max (25)
in the formula: p is dem,max Is an auxiliary variable representing the maximum demand value during the day;
the formula (21) is linearized by the following equation:
in the formula: n is a radical of p The number of the fan-shaped PQ semicircles is equal to that of the fan-shaped PQ semicircles, and the Q is more than or equal to 0; delta theta is the sector angle, (P) k ,Q k ) The coordinates of the division points of the fan shape and the PQ semicircle;
equation (24) is linearized as follows:
6. The method for robust energy management of a traction power supply system considering uncertain photovoltaic and load according to claim 5, wherein the two-stage robust optimization model for robust energy management of the traction power supply system established in the step 4 is as follows:
7. The method for managing the robust energy of the traction power supply system in consideration of the uncertain photovoltaic and load according to claim 6, wherein a main model and a sub model of the robust energy management model of the traction power supply system are formed through a column and constraint generation algorithm in the step 5, the main model and the sub model are solved in a circulating iteration mode to obtain the optimal charging and discharging power of the hybrid energy storage device in the worst scene, the optimal photovoltaic grid-connected power and the optimal power flow power of a back-to-back converter in a power flow controller, and therefore the robust energy management optimization of the traction power supply system is completed;
wherein, the expression of the main model is as follows:
s.t.x∈{0,1} (37)
in the formula: k is the number of iterative solution times, y l Is a first circulation time direction main modelThe decision variables that are added are the variables of the decision,to solve for the worst photovoltaic output obtained by the submodel,for solving the worst active load scenario, r, obtained for the submodel l * Representing the worst reactive load scene obtained by solving the submodel;
the sub-model expression is:
s.t.By≤d,(γ 1 ) (46)
Dy=e,(γ 2 ) (47)
Fy≤f-Ex * ,(γ 3 ) (48)
Gy≤p,(γ 4 ) (49)
Hy=a,(γ 5 ) (50)
Iy=r,(γ 6 ) (51)
in the formula: x is the number of * For the optimal solution of the main model, { gamma { 1 ,γ 2 ,γ 3 ,γ 4 ,γ 5 ,γ 6 Is a constraint dual variable;
the submodel equivalent representation method is as follows:
worst scenario p in sub-model * 、a * And r * To not determine the extreme values in sets P, A and R, equations (1) - (3) are therefore equivalent to:
based on strong dual theory, submodels (45) - (51) are equivalent to:
-B T γ 1 +D T γ 2 -F T γ 3 -G T γ 4 +H T γ 5 +I T γ 6 =c T (56)
γ 1 ≥0,γ 3 ≥0,γ 4 ≥0,γ 2 ,γ 5 ,γ 6 is a free variable (57)
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