IGDT-based traction power supply system day-ahead robust optimization scheduling method

Abstract

The invention discloses an IGDT-based traction power supply system day-ahead robust optimization scheduling method, and belongs to the field of power system optimization scheduling, and the method comprises the steps: taking the minimum daily comprehensive operation cost of a traction power supply system as a target, and building a deterministic day-ahead optimization operation model of a given photovoltaic output and traction load prediction value; based on the deterministic day-ahead optimization operation model, introducing an IGDT information gap decision theory, and establishing an IGDT robust optimization operation model for day-ahead operation of the traction power supply system, which considers scheduling decision, uncertainty set selection and operation cost control at the same time; and solving the IGDT robust optimization operation model to obtain a traction power supply system day-ahead robust optimization scheduling strategy. According to the method, the potential risk caused by relatively strong volatility and uncertainty of photovoltaic output and traction load is solved.

Description

Technical Field

[0001] The invention belongs to the field of power system optimization and dispatching, and in particular relates to a day-ahead robust optimization and dispatching method for a traction power supply system based on IGDT. Background Art

[0002] Photovoltaic power generation and hybrid energy storage systems are connected to the traction power supply system through the DC link provided by the back-to-back converter, which can not only realize the local consumption of photovoltaic resources along the railway, but also promote the recycling of regenerative braking energy and the peak-shaving and valley-filling of traction loads, and promote the realization of energy conservation, emission reduction and high-quality development of electrified railways. However, the volatility of traction loads and the intermittent nature of photovoltaic power generation make it difficult for power generation and load to achieve a dynamic balance between supply and demand, threatening the stable operation of the traction power supply system, especially the traction power supply system in the weak grid area in the western region. Therefore, it is necessary to study a day-ahead robust optimization scheduling strategy for the "source-grid-load-storage" traction power supply system based on IGDT to solve the potential risks brought about by the strong volatility and uncertainty of photovoltaic output and traction load. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a day-ahead robust optimization scheduling method for a traction power supply system based on IGDT, which solves the potential risks brought about by the strong volatility and uncertainty of photovoltaic output and traction load.

[0004] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a day-ahead robust optimization scheduling method for a traction power supply system based on IGDT, comprising:

[0005] With the goal of minimizing the daily comprehensive operating cost of the traction power supply system, a deterministic day-ahead optimization operation model is established for given PV output and traction load forecast values.

[0006] Based on the deterministic day-ahead optimization operation model, the IGDT information gap decision theory is introduced to establish an IGDT robust optimization operation model for the day-ahead operation of the traction power supply system, which takes into account scheduling decision, uncertainty set selection and operation cost control.

[0007] The IGDT robust optimization operation model is solved and the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

[0008] Furthermore, the expression of the deterministic day-ahead optimization operation model is:

[0009]

[0010]

[0011] Among them, min is the minimum function; C day is the daily operating cost of the traction substation; Cgrid is the electricity cost; C dem is the demand electricity cost; The operation and maintenance cost of the photovoltaic system; The operation and maintenance cost of the energy storage system; is the battery loss cost; N T is the total time period of the day-ahead optimization scheduling cycle; t is the time; m buy P is the electricity purchase price of the traction substation; t grid，+ The power purchased by the traction substation from the three-phase power grid; m fed is the feeding electricity price of traction substation; P t grid,- is the return power of the traction substation from the three-phase power grid; Δt is the scheduling step length of the day-ahead optimization stage; max is the maximum value function; P t dem is the demand power; is the maximum demand power; m pv is the operation and maintenance cost price of the photovoltaic system; P t pv is the photovoltaic power generation power; m b is the operation and maintenance cost price of lithium battery energy storage; P t b,ch is the charging power of the lithium battery energy storage element; P t b,dis is the discharge power of the lithium battery energy storage element; m sc is the operation and maintenance cost price of supercapacitor; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; The cost price of lithium battery loss.

[0012] Furthermore, the constraints of the deterministic day-ahead optimization operation model include system power balance constraints, PV constraints, HESS hybrid energy storage system constraints, BTBC constraints and voltage imbalance constraints:

[0013]

[0014]

[0015] Among them, P t grid，+ The power purchased by the traction substation from the three-phase power grid; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; M g is the maximum interaction power between the traction substation and the external power grid; P t grid,- is the return power of the traction substation from the three-phase power grid; max is the maximum value function; P t ld_L,+ is the traction power of the left power supply arm train; P t ld_R,+ P is the traction power of the right power supply arm train; t tr_L,+ It is the traction power transmitted to the left supply arm train through the V / v traction transformer; is the direction of power interaction between the left power supply arm of the traction transformer and the back-to-back converter. The power flowing into the left power supply arm of the traction transformer is 1, and the power flowing out of the left power supply arm of the traction transformer is 0; P t tr_L,- P is the power returned from the left power supply arm to the public grid; t ld_L,- is the braking power of the left power supply arm train; P t tr_R,+ It is the traction power transmitted to the right supply arm train through the V / v traction transformer; is the direction of power interaction between the right power supply arm of the traction transformer and the back-to-back converter. The power flowing into the right power supply arm of the traction transformer is 1, and the power flowing out of the right power supply arm of the traction transformer is 0; P t tr_R,- P is the power returned by the right power supply arm to the public grid; t ld_R,- is the braking power of the right power supply arm train; P t L～α is the interaction power between the left power supply arm and the α converter; P t α～L is the interaction power between the α converter and the left power supply arm; is the direction of power interaction between the back-to-back α converter and the traction transformer, the power flowing into the α converter is 1, and the power flowing out of the α converter is 0; is the rated capacity limit of the back-to-back converter; P t R～β is the interaction power between the right power supply arm and the β converter; P t β～R is the interaction power between the β converter and the right power supply arm; is the direction of power interaction between the back-to-back β converter and the traction transformer, the power flowing into the β converter is 1, and the power flowing out of the β converter is 0; P t pv is the photovoltaic power generation power; P pv,f The upper limit of the photovoltaic output prediction value; is the state of charge of the lithium battery energy storage element at time t; is the state of charge of the lithium battery energy storage element at time t-1; η b,ch is the charging efficiency of lithium battery energy storage element; P t b,ch is the charging power of the lithium battery energy storage element; Δt is the scheduling step length of the day-ahead optimization stage; P t b,dis is the discharge power of the lithium battery energy storage element; η b,dis is the discharge efficiency of the lithium battery energy storage element; is the rated capacity of the lithium battery energy storage element; is the charge state of the supercapacitor energy storage element at time t; is the state of charge of the supercapacitor energy storage element at time t-1; η sc,ch is the charging efficiency of the supercapacitor energy storage element; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; η sc,dis is the discharge efficiency of the supercapacitor energy storage element; is the rated capacity of the supercapacitor energy storage element; It is the lower limit of the state of charge of the lithium battery energy storage element; It is the upper limit of the state of charge of the lithium battery energy storage element; The state of charge of the lithium battery energy storage element at the beginning; The state of charge of the lithium battery energy storage element at the end of the process; It is the lower limit of the state of charge of the supercapacitor energy storage element; is the upper limit of the state of charge of the supercapacitor energy storage element; is the charge state of the supercapacitor energy storage element at the beginning; is the charge state of the supercapacitor energy storage element at the end of the process; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. is the rated power of the lithium battery; It is a binary state variable. When it is equal to 1, it means that the supercapacitor is in the charging state, and when it is equal to 0, it means that the supercapacitor is in the discharging state. is the rated power of the supercapacitor; a i 、b i and c i are the coefficients of the regular dodecagon linearized power flow constraint; P t btbc,L～α is the interactive active power between the left power supply arm of the back-to-back converter and the α converter; P t btbc,α～Lis the interactive active power between the α converter and the left power supply arm of the back-to-back converter; P t btbc,R～β is the interactive active power between the right power supply arm of the back-to-back converter and the β converter; P t btbc ,β～R is the interactive active power between the β converter and the right power supply arm of the back-to-back converter; is the reactive power of α converter; is the reactive power of β converter; is the rated capacity of the α converter; is the rated capacity of the β converter; P t tr_L P is the active power delivered by the traction transformer to the left power supply arm; t α is the active power generated by the α-phase converter; P t ld_L is the active power of the left power supply arm train; The reactive power delivered to the left supply arm by the traction transformer; is the reactive power generated by the α-phase converter; is the reactive power of the left power supply arm train; P t tr_R The active power delivered to the right supply arm by the traction transformer; is the active power generated by the β-phase converter; P t ld_R is the active power of the right power supply arm train; The reactive power delivered to the right supply arm by the traction transformer; is the reactive power generated by the β phase converter; is the reactive power of the right power supply arm train; is the upper limit of voltage imbalance; S d is the short-circuit capacity of the external power grid.

[0016] Furthermore, the expression of the IGDT robust optimization operation model is:

[0017]

[0018] y={P t grid，+ ,P t grid,- ,P t tr_L,+ ,P t tr_L,- ,P t tr_R,- ,P t tr_R,+ ,P tL～α ,P t α～L ,

[0019]

[0020] in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; x is the binary state variable vector in the deterministic day-ahead optimization operation model; X is the feasible domain of x; is the maximization function about x and ξ; u is the uncertainty variable; ξ is the deviation ratio of the uncertainty variable u; is the maximization function with respect to u; is the minimization function about y; y is the continuous variable vector in the deterministic day-ahead optimization operation model; Y(x,u) is the feasible domain of y; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C day is the daily operating cost of the traction substation; C0 is the system operating cost under the deterministic operating environment; A is the coefficient matrix of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; κ is the constant vector of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; R is a real number set; E is the coefficient matrix of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; b is the constant vector of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; K is the inequality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model ; z is the constant vector of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; F is the coefficient matrix of inequality constraints on variable vector x in the constraints of the deterministic day-ahead optimization operation model; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; h is the constant vector of inequality constraints on variable vectors x and y in the constraints of the deterministic day-ahead optimization operation model; J is the coefficient matrix of equality constraints between variable vector y and uncertain variable u in the constraints of the deterministic day-ahead optimization operation model; Ω is the feasible domain of uncertain variable u; is the predicted value of the uncertainty variable u; Γ is the uncertainty budget; is the minimization function about x in a deterministic environment; C is the system operation cost in a deterministic operating environment; P pv,f The upper limit of the photovoltaic output prediction value; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. is a binary state variable. When it is equal to 1, it means that the supercapacitor is in a charging state, and when it is equal to 0, it means that the supercapacitor is in a discharging state. t grid，+ P is the power purchased by the traction substation from the three-phase power grid; t grid,- P is the return power from the three-phase power grid to the traction substation; t tr_L,+ P is the traction power transmitted to the left power supply arm train through the V / v traction transformer; t tr _L,- P is the power returned from the left power supply arm to the public grid; t tr_R,+ P is the traction power transmitted to the right power supply arm train through the V / v traction transformer; t tr_R,- P is the power returned by the right power supply arm to the public grid; t L～α is the interaction power between the left power supply arm and the α converter; P t α～L is the interaction power between the α converter and the left power supply arm; P t R～β is the interaction power between the right power supply arm and the β converter; P t β～R is the interaction power between the β converter and the right power supply arm; P t pv is the photovoltaic power generation power; P t b,ch is the charging power of the lithium battery energy storage element; P t b,dis is the discharge power of the lithium battery energy storage element; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; is the reactive power generated by the α-phase converter; is the reactive power generated by the β phase converter; The reactive power delivered to the left supply arm by the traction transformer; It is the reactive power delivered by the traction transformer to the right supply arm.

[0021] Furthermore, the IGDT robust optimization operation model is solved to obtain the day-ahead robust optimization scheduling strategy of the traction power supply system, which is specifically:

[0022] The IGDT robust optimization operation model is rewritten as a two-stage decision problem; the two-stage decision problem includes a main problem MP and a sub-problem SP;

[0023] The C&CG algorithm embedded in the CPLEX solver is used to iteratively solve the main-subproblems of the two-stage decision-making problem. When the error between the optimal solutions of the main problem is less than the set value through continuous iteration, the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

[0024] Furthermore, the expression of the main problem MP is:

[0025]

[0026] in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; is the maximization function about x; x is the binary state variable vector in the deterministic optimization scheduling model; X is the feasible domain of x; ξ is the deviation ratio of the uncertainty variable u; η is an auxiliary variable, which represents the actual operating cost in the worst case. The worst case is when the load fluctuation is certain and the photovoltaic output is the smallest in the uncertainty concentration, and the operating cost is the largest; y l is the scheduling decision for each iteration after solving the subproblem; u l is the uncertain variable value under the worst case; C0 is the system operation cost under the deterministic operating environment; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C day is the daily operating cost of the traction substation; Y(x,u l ) is y l The feasible domain of for u l The feasible domain of is the cost deviation factor in the worst case; l is the scheduling decision and the worst case index; Ψ is the current iteration number.

[0027] Furthermore, the expression of the sub-problem SP is:

[0028]

[0029] in, is the bilinear optimization model function of the sub-problem of the day-ahead robust optimization scheduling method for the IGDT-based traction power supply system; x is the binary state variable vector in the deterministic optimization scheduling model; ξ is the deviation ratio of the uncertainty variable u; is the maximization function about u; u is the uncertainty variable; Ω is the feasible domain of the uncertainty variable u;

[0030] is an auxiliary variable used to replace the bilinear term μ is the dual variable corresponding to the equality constraint of variable vector y; ω is the dual variable corresponding to the inequality constraint of variable vector y; π is the dual variable corresponding to the inequality constraint containing variable vectors x and y; σ is the dual variable corresponding to the equality constraint containing variable vectors y and u; y is the continuous variable vector in the deterministic optimization scheduling model; b is the constant vector of equality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; z is the constant vector of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; h is the constant vector of inequality constraints on variable vectors x and y in the constraints of the deterministic day-ahead optimization operation model; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; E

[0031] is the coefficient matrix of the equality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; K is the coefficient matrix of the inequality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; F is the coefficient matrix of the inequality constraint on the variable vector x in the constraint conditions of the deterministic day-ahead optimization operation model; J is the coefficient matrix of the equality constraint between the variable vector y and the uncertain variable u in the constraint conditions of the deterministic day-ahead optimization operation model; is a binary auxiliary variable; M is a constant.

[0032] The beneficial effects of the present invention are as follows: based on the deterministic scheduling model framework, the information gap decision theory is introduced to establish an IGDT robust optimization operation model for the day-ahead operation of the traction power supply system, which simultaneously considers scheduling decisions, uncertainty set selection and operation cost control, so as to cope with the impact of distributed photovoltaic uncertainty on the stable and economic operation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 The figure is a flow chart of the method of the present invention.

[0034] Figure 2 It is a schematic diagram of linearization of a regular dodecagon inscribed in a circle according to the present invention.

[0035] Figure 3 It is a vector diagram of the BTBC negative sequence symmetric compensation principle in an embodiment of the present invention.

[0036] Figure 4 Schematic diagram of worst-case photovoltaic power generation under different β in an embodiment of the present invention.

[0037] Figure 5Schematic diagram of comparing the robust optimization effects of the system under different cost deviations in the embodiments of the present invention.

[0038] Figure 6 It is a schematic diagram of the system's adaptation to photovoltaic output fluctuations under different photovoltaic configurations in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0040] Example 1

[0041] like Figure 1 As shown, in one embodiment of the present invention, a day-ahead robust optimization scheduling method for a traction power supply system based on IGDT includes:

[0042] With the goal of minimizing the daily comprehensive operating cost of the traction power supply system, a deterministic day-ahead optimization operation model is established for given PV output and traction load forecast values.

[0043] Based on the deterministic day-ahead optimization operation model, the IGDT information gap decision theory is introduced to establish an IGDT robust optimization operation model for the day-ahead operation of the traction power supply system, which takes into account scheduling decision, uncertainty set selection and operation cost control.

[0044] The IGDT robust optimization operation model is solved and the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

[0045] The expression of the deterministic day-ahead optimization operation model is:

[0046]

[0047] Among them, min is the minimum function; C day is the daily operating cost of the traction substation; C grid is the electricity cost; C dem is the demand electricity cost; The operation and maintenance cost of the photovoltaic system; The operation and maintenance cost of the energy storage system; is the battery loss cost; N T is the total time period of the day-ahead optimization scheduling cycle; t is the time; m buy P is the electricity purchase price of the traction substation; t grid，+The power purchased by the traction substation from the three-phase power grid; m fed is the feeding electricity price of traction substation; P t grid,- is the return power of the traction substation from the three-phase power grid; Δt is the scheduling step length of the day-ahead optimization stage; max is the maximum value function; P t dem is the demand power; is the maximum demand power; m pv is the operation and maintenance cost price of the photovoltaic system; P t pv is the photovoltaic power generation power; m b is the operation and maintenance cost price of lithium battery energy storage; P t b,ch is the charging power of the lithium battery energy storage element; P t b,dis is the discharge power of the lithium battery energy storage element; m sc is the operation and maintenance cost price of supercapacitor; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; The cost price of lithium battery loss.

[0048] The constraints of the deterministic day-ahead optimization operation model include system power balance constraints, PV constraints, HESS hybrid energy storage system constraints, BTBC constraints and voltage imbalance constraints:

[0049]

[0050] Among them, P t grid，+ The power purchased by the traction substation from the three-phase power grid; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; M g is the maximum interaction power between the traction substation and the external power grid; P t grid,- is the return power of the traction substation from the three-phase power grid; max is the maximum value function; P t ld_L,+ is the traction power of the left power supply arm train; P t ld_R,+ P is the traction power of the right power supply arm train; t tr_L,+ It is the traction power transmitted to the left supply arm train through the V / v traction transformer; is the direction of power interaction between the left power supply arm of the traction transformer and the back-to-back converter. The power flowing into the left power supply arm of the traction transformer is 1, and the power flowing out of the left power supply arm of the traction transformer is 0; P t tr_L,- P is the power returned from the left power supply arm to the public grid; t ld_L,- is the braking power of the left power supply arm train; P t tr_R,+ It is the traction power transmitted to the right supply arm train through the V / v traction transformer; is the direction of power interaction between the right power supply arm of the traction transformer and the back-to-back converter. The power flowing into the right power supply arm of the traction transformer is 1, and the power flowing out of the right power supply arm of the traction transformer is 0; P t tr_R,- P is the power returned by the right power supply arm to the public grid; t ld_R,- is the braking power of the right power supply arm train; P t L～α is the interaction power between the left power supply arm and the α converter; P t α～L is the interaction power between the α converter and the left power supply arm; is the direction of power interaction between the back-to-back α converter and the traction transformer, the power flowing into the α converter is 1, and the power flowing out of the α converter is 0; is the rated capacity limit of the back-to-back converter; P t R～β is the interaction power between the right power supply arm and the β converter; P t β～R is the interaction power between the β converter and the right power supply arm; is the direction of power interaction between the back-to-back β converter and the traction transformer, the power flowing into the β converter is 1, and the power flowing out of the β converter is 0; P t pv is the photovoltaic power generation power; P pv,f The upper limit of the photovoltaic output prediction value; is the state of charge of the lithium battery energy storage element at time t; is the state of charge of the lithium battery energy storage element at time t-1; η b,ch is the charging efficiency of lithium battery energy storage element; P t b,ch is the charging power of the lithium battery energy storage element; Δt is the scheduling step length of the day-ahead optimization stage; P t b,dis is the discharge power of the lithium battery energy storage element; η b,dis is the discharge efficiency of the lithium battery energy storage element; is the rated capacity of the lithium battery energy storage element; is the charge state of the supercapacitor energy storage element at time t; is the state of charge of the supercapacitor energy storage element at time t-1; η sc,ch is the charging efficiency of the supercapacitor energy storage element; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; η sc,dis is the discharge efficiency of the supercapacitor energy storage element; is the rated capacity of the supercapacitor energy storage element; It is the lower limit of the state of charge of the lithium battery energy storage element; It is the upper limit of the state of charge of the lithium battery energy storage element; The state of charge of the lithium battery energy storage element at the beginning; The state of charge of the lithium battery energy storage element at the end of the process; It is the lower limit of the state of charge of the supercapacitor energy storage element; is the upper limit of the state of charge of the supercapacitor energy storage element; is the charge state of the supercapacitor energy storage element at the beginning; is the charge state of the supercapacitor energy storage element at the end of the process; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. is the rated power of the lithium battery; It is a binary state variable. When it is equal to 1, it means that the supercapacitor is in the charging state, and when it is equal to 0, it means that the supercapacitor is in the discharging state. is the rated power of the supercapacitor; a i 、b i and c i are the coefficients of the regular dodecagon linearized power flow constraint; P t btbc,L～α is the interactive active power between the left power supply arm of the back-to-back converter and the α converter; P t btbc,α～L is the interactive active power between the α converter and the left power supply arm of the back-to-back converter; P t btbc,R～β is the interactive active power between the right power supply arm of the back-to-back converter and the β converter; P t btbc ,β～R is the interactive active power between the β converter and the right power supply arm of the back-to-back converter; is the reactive power of α converter; is the reactive power of β converter; is the rated capacity of the α converter; is the rated capacity of the β converter; P t tr_LP is the active power delivered by the traction transformer to the left power supply arm; t α is the active power generated by the α-phase converter; P t ld_L is the active power of the left power supply arm train; The reactive power delivered by the traction transformer to the left power supply arm; Q t α is the reactive power generated by the α-phase converter; is the reactive power of the left power supply arm train; P t tr_R P is the active power delivered by the traction transformer to the right power supply arm; t β is the active power generated by the β-phase converter; P t ld_R is the active power of the right power supply arm train; The reactive power delivered to the right supply arm by the traction transformer; is the reactive power generated by the β phase converter; is the reactive power of the right power supply arm train; is the upper limit of voltage imbalance; S d is the short-circuit capacity of the external power grid.

[0051] The expression of the IGDT robust optimization operation model is:

[0052]

[0053] in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; x is the binary state variable vector in the deterministic day-ahead optimization operation model; X is the feasible domain of x; is the maximization function about x and ξ; u is the uncertainty variable; ξ is the deviation ratio of the uncertainty variable u; is the maximization function with respect to u; is the minimization function about y; y is the continuous variable vector in the deterministic day-ahead optimization operation model; Y(x,u) is the feasible domain of y; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C dayis the daily operating cost of the traction substation; C0 is the system operating cost under the deterministic operating environment; A is the coefficient matrix of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; κ is the constant vector of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; R is a real number set; E is the coefficient matrix of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; b is the constant vector of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; K is the inequality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model ; z is the constant vector of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; F is the coefficient matrix of inequality constraints on variable vector x in the constraints of the deterministic day-ahead optimization operation model; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; h is the constant vector of inequality constraints on variable vectors x and y in the constraints of the deterministic day-ahead optimization operation model; J is the coefficient matrix of equality constraints between variable vector y and uncertain variable u in the constraints of the deterministic day-ahead optimization operation model; Ω is the feasible domain of uncertain variable u; is the predicted value of the uncertainty variable u; Γ is the uncertainty budget; is the minimization function about x in a deterministic environment; C is the system operation cost in a deterministic operating environment; P pv,f The upper limit of the photovoltaic output prediction value; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. is a binary state variable. When it is equal to 1, it means that the supercapacitor is in a charging state, and when it is equal to 0, it means that the supercapacitor is in a discharging state. t grid，+ P is the power purchased by the traction substation from the three-phase power grid; t grid,- P is the return power from the three-phase power grid to the traction substation; t tr_L,+ P is the traction power transmitted to the left power supply arm train through the V / v traction transformer; t tr _L,- P is the power returned from the left power supply arm to the public grid; t tr_R,+ P is the traction power transmitted to the right power supply arm train through the V / v traction transformer;t tr_R,- P is the power returned by the right power supply arm to the public grid; t L～α is the interaction power between the left power supply arm and the α converter; P t α～L is the interaction power between the α converter and the left power supply arm; P t R～β is the interaction power between the right power supply arm and the β converter; P t β～R is the interaction power between the β converter and the right power supply arm; P t pv is the photovoltaic power generation power; P t b,ch is the charging power of the lithium battery energy storage element; P t b,dis is the discharge power of the lithium battery energy storage element; P t sc,ch is the charging power of the supercapacitor energy storage element; P t sc,dis is the discharge power of the supercapacitor energy storage element; is the reactive power generated by the α-phase converter; is the reactive power generated by the β phase converter; The reactive power delivered to the left supply arm by the traction transformer; It is the reactive power delivered by the traction transformer to the right supply arm.

[0054] The robust optimization operation model of IGDT is solved to obtain the robust optimization scheduling strategy of the traction power supply system, which is specifically:

[0055] The IGDT robust optimization operation model is rewritten as a two-stage decision problem; the two-stage decision problem includes a main problem MP and a sub-problem SP;

[0056] The C&CG algorithm embedded in the CPLEX solver is used to iteratively solve the main-subproblems of the two-stage decision-making problem. When the error between the optimal solutions of the main problem is less than the set value through continuous iteration, the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

[0057] The expression of the main problem MP is:

[0058]

[0059] in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; is the maximization function about x; x is the binary state variable vector in the deterministic optimization scheduling model; X is the feasible domain of x; ξ is the deviation ratio of the uncertainty variable u; η is an auxiliary variable, which represents the actual operating cost in the worst case. The worst case is when the load fluctuation is certain and the photovoltaic output is the smallest in the uncertainty concentration, and the operating cost is the largest; y l is the scheduling decision for each iteration after solving the subproblem; u l is the uncertain variable value under the worst case; C0 is the system operation cost under the deterministic operating environment; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C day is the daily operating cost of the traction substation; Y(x,u l ) is y l The feasible domain of for u l The feasible domain of is the cost deviation factor in the worst case; l is the scheduling decision and the worst case index; Ψ is the current iteration number.

[0060] The expression of the sub-problem SP is:

[0061]

[0062] in, is the bilinear optimization model function of the sub-problem of the day-ahead robust optimization scheduling method for the IGDT-based traction power supply system; x is the binary state variable vector in the deterministic optimization scheduling model; ξ is the deviation ratio of the uncertainty variable u; is the maximization function about u; u is the uncertainty variable; Ω is the feasible domain of the uncertainty variable u;

[0063] is an auxiliary variable used to replace the bilinear term μ is the dual variable corresponding to the equality constraint of the variable vector y; ω is the dual variable corresponding to the inequality constraint of the variable vector y; π is the dual variable corresponding to the inequality constraint containing the variable vectors x and y; σ is the dual variable corresponding to the equality constraint containing the variable vectors y and u; y is the continuous variable vector in the deterministic optimization scheduling model; b is the constant vector of the equality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; z is the constant vector of the inequality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; h is the constant vector of the inequality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model The constant vector of inequality constraints on vectors x and y; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; E is the coefficient matrix of equality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; K is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; F is the coefficient matrix of inequality constraints on variable vector x in the constraints of the deterministic day-ahead optimization operation model; J is the coefficient matrix of equality constraints between variable vector y and uncertain variable u in the constraints of the deterministic day-ahead optimization operation model; is a binary auxiliary variable; M is a constant.

[0064] Example 2

[0065] In one embodiment of the present invention, a method for day-ahead robust optimization scheduling of a traction power supply system based on IGDT comprises the following steps:

[0066] S1. With the goal of minimizing the system's daily comprehensive operating cost, a deterministic day-ahead optimization operation model with given PV output and traction load forecast values ​​was established;

[0067] S2. Based on the deterministic scheduling model framework, the information gap decision theory is introduced to establish an IGDT robust optimization operation model for the day-ahead operation of the traction power supply system, which simultaneously considers scheduling decision, uncertainty set selection and operation cost control.

[0068] In this embodiment, taking an electrified railway traction substation in western my country as an example, a case analysis is performed based on the software platform MATLABR2019b (with built-in optimization toolbox YALMIP and optimization solver CPLEX).

[0069] The step S1 is specifically as follows:

[0070] S101. Day-ahead economic optimization operation aims to minimize the daily operating cost of the traction substation, including the electricity cost, demand cost, photovoltaic-storage system operation and maintenance cost, and battery loss cost. The expression is:

[0071]

[0072] In the formula, m buy 、m fed Respectively represent the purchase price and feed-in price of the traction substation; P t grid，+ , P t grid,- Respectively represent the power purchased and returned by the traction substation from the three-phase power grid; m pv 、m b 、m sc Respectively represent the operation and maintenance cost price of photovoltaic system, lithium battery energy storage and supercapacitor; m dem is the demand electricity price, P t dem is the required power; P t pv is the photovoltaic power generation power; P t b,ch , P t b,dis , P t sc,ch , P t sc,dis is the charging and discharging power of each energy storage element; is the lithium battery loss cost price, and this embodiment has made a detailed calculation description; Δt is the scheduling step length of the day-ahead optimization stage, which is set to 1 minute; N T is the total time period of the day-ahead optimization scheduling cycle, which is 1440.

[0073] It should be noted that the maximum demand power is the maximum average value of the power purchased by the traction substation every 15 minutes within a month. When the train operation schedule is fixed within a month, the traction load of the electric locomotive has daily repeatability. Therefore, the monthly maximum demand is averaged to a single day and calculated using the sliding method. The value range of t is 1 to N T -14. In order to reduce the complexity of model solution, an auxiliary time-independent variable is introduced To represent the daily peak demand power, the demand electricity cost shown in formula (3) is linearized and expressed as:

[0074]

[0075] S102. Based on the cost function in S101, consider the constraints.

[0076] (1) System power balance constraints

[0077] In the "source-grid-load-storage" traction power supply system, all traction loads are powered by the external grid, photovoltaic power generation system PV and hybrid energy storage system HESS through V / v traction transformers and back-to-back converters BTBC. Therefore, according to the system power flow distribution law, the active and reactive power balance constraints of each node are:

[0078]

[0079] In the formula, is a binary variable, The incoming power direction of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns power to the external power grid, P t ld_L,+ , P t ld _L,- , P t ld_R,+ , P t ld_R,- are the traction power and braking power of the left and right power supply arms respectively; P t tr_L,- , P t tr_R,- are the power returned to the public grid by the left and right power supply arms respectively; P t α～L , P t L～α , P t β～R , P t R～β are the interaction powers between the left power supply arm and the α converter, and between the right power supply arm and the β converter; M g It is the maximum interactive power between the traction substation and the external power grid, which is limited by the transformer capacity; They represent the directions of power interaction between the left and right supply arms of the V / v traction transformer and the back-to-back α and β converters respectively; is the rated capacity limit of the back-to-back converter.

[0080] (2) PV Constraint

[0081] During the day-ahead dispatch phase, the photovoltaic output power is constrained by the output forecast upper limit.

[0082] 0≤P t pv ≤P pv，f (11)

[0083] Where P pv,f It is the upper limit of the predicted photovoltaic output.

[0084] (3) HESS constraints

[0085] During steady-state operation, the dynamic operating constraints of the state of charge caused by HESS charging and discharging must be met first:

[0086]

[0087] In the formula, Indicates the charge state of each energy storage element at time t; P t b,ch , P t b,dis , P t sc,ch , P t sc,dis Represents the charging and discharging power of each energy storage element at time t; η b,ch , η b,dis , η sc,ch , η sc,dis are the corresponding charging and discharging efficiencies respectively; are the rated capacity of each energy storage element respectively.

[0088] Secondly, the state of charge in the time interval t should be within the predefined upper and lower limits to avoid overcharging and overdischarging of the energy storage element, thereby extending its cycle life. At the same time, in order to facilitate the daily scheduling of the system, the state of charge of the energy storage system is required to be equal at the beginning and end of each day, that is:

[0089]

[0090] In the formula, are the upper and lower limits of the state of charge of each energy storage element respectively; are the SOC values ​​of each energy storage component at the beginning and end moments respectively.

[0091] In addition, within any time interval, the charge and discharge power of batteries and supercapacitors are limited by their physical properties, that is, any energy storage element can only perform charging or discharging operations during operation, so the specific constraints are as follows:

[0092]

[0093] In the formula, It is a binary state variable. When it is equal to 1, it means that the battery or supercapacitor is in a charging state. When it is equal to 0, it means that the battery or supercapacitor is in a discharging state. Represent the rated power of the battery and supercapacitor respectively.

[0094] (4) BTBC constraints

[0095] For the traction power supply system after the solar-storage connection, the active and reactive compensation power that BTBC can provide is subject to its rated capacity. The restrictions are:

[0096]

[0097] In the formula, are the reactive powers generated by the α and β phase converters, respectively. The BTBC capacity constraint is mathematically expressed as the interior of the PQ circle composed of active power and reactive power. It is simplified to the form shown in equation (19) in the rectangular coordinate system and is nonlinear in calculation.

[0098] x 2 +y 2 ≤r (19)

[0099] Using the linearization method of regular polygon approximation, the circular constraint is replaced by multiple straight lines through the regular polygon inscribed in the circle. The specific linearization process is as follows: Figure 2 shown.

[0100] Figure 2 In the figure, the 12 straight line constraints of the regular dodecagon can be expressed in the following form in the rectangular coordinate system:

[0101] a i x+b i y+c i r≤0 (20)

[0102] Similarly, the nonlinear circular constraint (18) can be approximately transformed into a regular dodecagonal linear constraint equation system as shown in equation (21):

[0103]

[0104] Where i is the line number, and the numbering sequence is as follows: Figure 2 The numbers are shown counterclockwise; P t btbc,L～α , P t btbc,α～L They are respectively represented as the interactive active power of the left power supply arm of the back-to-back converter and the α converter; P t btbc,R～β , P t btbc,β～R They are respectively represented as the interactive active power between the right power supply arm of the back-to-back converter and the β converter; are the reactive powers of α and β converters respectively; are the rated capacities of α and β converters respectively, a i 、b i 、c i is the coefficient of the regular dodecagon linearized power flow constraint, and the coefficient values ​​are shown in Table 1.

[0105] Table 1 System operating conditions

[0106]

[0107]

[0108] (5) Voltage imbalance constraint

[0109] The increasing power demand of high-power traction loads in the western plateau region has put forward higher requirements on the power supply capacity of the external regional power grid. At the same time, the inherent imbalance of the V / V traction transformer will produce a large negative sequence current that threatens the stability of the regional power grid. Therefore, the present invention particularly considers the problem of three-phase voltage imbalance caused by negative sequence current, and introduces three-phase voltage imbalance constraints in the dispatching model. According to my country's power quality standard GB / T 15543-2008, the three-phase voltage imbalance caused by negative sequence current at the PCC can be expressed as:

[0110]

[0111] Where U AB , S d They are the rated line voltage (kV) and short-circuit capacity (MVA) of the external power grid respectively; is the current of the external power grid; The upper limit of voltage imbalance is 1.3%.

[0112] According to the voltage and current vector relationship between the primary and secondary sides of the V / V traction transformer, the negative sequence current expression is:

[0113]

[0114] In the formula, is the current vector of the external power grid; N TT is the turns ratio of the V / v traction transformer; I α ,I β are the currents flowing through the left and right power supply arms respectively; is the current vector flowing through the left and right power supply arms.

[0115] Furthermore, by substituting equation (23) into equation (22), the voltage unbalance constraint expression can be obtained:

[0116]

[0117] The BTBC symmetrical compensation method is used to linearize equation (24), that is, the active and reactive power of the left and right power supply arms of the V / v traction transformer are equal through the active and reactive power compensation of the back-to-back converter, that is:

[0118]

[0119] Figure 3 This is the negative sequence compensation process of BTBC. The system voltage and current phasor relationship before compensation is as follows: Figure 3 As shown in (a), during the actual operation of the electric locomotive, the traction loads on the left and right power supply arms are generally not equal, causing asymmetry of the three-phase current in the public power grid, and then generating a large amount of negative sequence current. The voltage and current phasor transfer during the BTBC negative sequence compensation process is shown in Figure 2. Figure 3 (b) shows: first compensate the reactive current and To unity power factor, so that the voltage and current phases of the power supply arm are consistent; then compensate the active current and Make the active power of the two-phase feeder balanced; then compensate for the reactive current and Adjust the current phase of the power supply arm so that the current of the left and right power supply arms after compensation With three-phase voltage There is a phase difference and And make the compensation current amplitude equal, so as to achieve negative sequence compensation and reduce the three-phase imbalance on the grid side to below the national standard requirements.

[0120] Therefore, the nonlinear square root constraint (24) can be linearly expressed as:

[0121]

[0122] In this embodiment, a certain electrified railway traction substation in western my country is taken as an example to draw the day-ahead traction load and maximum photovoltaic output curve. Tables 2 to 4 give the parameters of the traction substation, photovoltaic-hybrid energy storage system and electricity billing standards, among which the electricity fed back to the grid adopts the "reverse delivery and positive billing" billing scheme, that is, the electricity is fed back to the grid and a penalty electricity fee is charged. In addition, the operation and maintenance cost price of the photovoltaic-energy storage system is 0.05 yuan / kWh.

[0123] Table 2 Two-part electricity price parameters

[0124]

[0125] Table 3 Traction substation parameters

[0126]

[0127] Table 4 Hybrid energy storage system parameters

[0128]

[0129] The step S2 is specifically as follows:

[0130] S201. IGDT is an interval optimization method for models with uncertain parameters. Unlike random programming methods that rely on a large amount of historical data and precise probability density functions, it can quantify uncertainty when the probability distribution and fluctuation range of uncertain parameters are unknown. IGDT theory includes risk avoidance strategy and risk preference strategy. In order to better deal with the adverse effects of source-load uncertainty on the operation of the traction power supply system, the present invention adopts the former, i.e., a more conservative robust strategy, to establish an IGDT robust optimization operation model, and provide a scheduling plan reference for decision makers.

[0131] For the optimization problem with uncertain parameters, it can be expressed as:

[0132]

[0133] Where f is the objective function of the day-ahead optimization operation; x and κ are uncertainty parameters and decision variables, respectively; h and g represent the equality and inequality constraints in the deterministic economic dispatch model, respectively; l is the number of equations; g , are the upper and lower limits of the inequality in the deterministic economic dispatch model. Assuming that the uncertainty set Ω is the feasible domain of x, the envelope constraint model of the fluctuation of uncertainty parameters within a certain range can be expressed as:

[0134]

[0135] In the formula, ξ is the predicted value and deviation ratio of the uncertainty variable x, where ξ>0; Γ is the “uncertainty budget”, which aims to control the conservatism of the proposed scheduling plan and has a value range of [0,N T ], the larger Γ is, the stronger the robustness is and the higher the operating cost is.

[0136] Assume a deterministic operating environment, that is, x is The optimal objective function value is f0, and the maximum acceptable objective cost of the decision maker after considering the uncertainty parameters is f c , then the robust optimization operation model based on IGDT can be expressed as:

[0137]

[0138] In the formula, ε c Cost deviation factor for decision makers, ε c The larger the f c The larger it is, the higher the risk aversion is and the more robust the scheduling decision is. h and g represent the equality and inequality constraints that the decision variables should satisfy, respectively.

[0139] S202. During the actual operation of the traction power supply system, there are many uncertain factors, which affect the stability and economic benefits of the system operation to a certain extent. The present invention takes into account the uncertainty of photovoltaic output and traction load. When the train schedule is fixed (except for major holidays), the traction load has daily repeatability and relatively small randomness, and a high-precision prediction can be achieved before day-ahead scheduling. In other words, the uncertainty setting of the traction load can be easily predefined without worrying about unexpected extreme situations. Therefore, in the day-ahead scheduling stage, the present invention considers that the uncertainty set of the traction load is fixed, while the uncertainty set of photovoltaic power generation is optimizable.

[0140] In view of the uncertain operating environment shown in formula (29), a robust optimization operation model of IGDT is established to make the system more flexible and adaptable in the face of uncertain fluctuations. For the convenience of representation, the deterministic optimization scheduling model established in S201 is expressed in a compact form of matrix and vector, as follows:

[0141]

[0142] In the formula, x and y represent the binary state variable vector (v ～ ) and a continuous variable vector (P ～ , Q ～ ); u is the uncertainty variable, namely the photovoltaic power generation power and the traction load power; X, Y and Ω are the feasible domains of x, y and u respectively; b, c, d, f, h, A, E, K, F, G, J are the parameter vector and parameter matrix respectively.

[0143] Based on the IGDT framework, the objective function of the deterministic optimization scheduling model in S201 is transformed into the IGDT robust function shown in the following formula:

[0144]

[0145] In the formula, C0 is the system operation cost in a deterministic operating environment, which can be calculated by formula (32) and used as the reference cost for scheduling decision makers; is the cost deviation factor, which indicates the increased proportion of the operating cost budget.

[0146]

[0147] Therefore, the IGDT robust optimization operation model that meets the operating cost budget constraint and robustness requirements can be fully expressed as Equation (33). This model embeds the uncertainty set selection ξ and the uncertainty budget Γ into the scheduling decision, avoiding the over-conservatism of the scheduling decision and the infeasibility caused by improper uncertainty set selection.

[0148]

[0149] S203, based on the IGDT robust optimization operation model in S302, the solution is obtained. Since it is a complex "max-max-min" three-layer optimization problem, it is difficult for the existing solver to solve it directly. Therefore, the present invention introduces an auxiliary variable η to represent the second-stage operation cost in the worst case, rewrites the model into a two-stage decision problem, and adopts a column constraint generation (C&CG) algorithm with fast convergence speed and few iterations to solve it. The model is rewritten as follows:

[0150]

[0151] The scheduling model includes three types of decision variables, among which the first-level decision variables include the first-stage scheduling plan x, photovoltaic power generation power deviation ratio ξ and auxiliary variables η; the second-level decision variable is the uncertainty variable u, that is, photovoltaic power generation; the third-level decision variable is the second-stage scheduling plan y. The inner "min" problem aims to minimize the system operating cost given the first-level and second-level decision variables, and the "max" problem aims to maximize the minimization value and derive the worst case in the uncertain set Ω; the outer "max" problem aims to find the optimal first-level decision variable when the cost deteriorates.

[0152] According to the master-subproblem framework of the C&CG algorithm, the master problem (MP) of the original problem (33) is the first-stage decision in the model (34), which can be expressed as:

[0153]

[0154] Where Ψ is the current iteration number; y l and u l They are the second-stage scheduling decision in each iteration after solving the subproblem and the uncertain variable values ​​in the worst case.

[0155] Similarly, the subproblem (SP) of the original problem (33) is an inner-level “max-min” two-level linear programming problem, namely:

[0156]

[0157] Where μ, ω, π, and σ are the dual variables corresponding to the relevant constraints.

[0158] Given the feasible domain Y, the inner min problem of the subproblem is a linear problem, which can be transformed into a max problem according to the strong duality theory and the duality relation of related constraints. Therefore, the subproblem (SP) can be restated as the following bilinear optimization model:

[0159]

[0160] It should be noted that the optimal solution of u will appear at the extreme point of the uncertainty set Ω, and the IGDT uncertainty set Ω changes with the change of the photovoltaic uncertainty ξ, making the number of extreme points infinite, which in turn limits the solution efficiency of the C&CG algorithm. In actual scheduling, at any time interval, when the photovoltaic power generation is equal to the predicted value or its lower bound, and the traction load is equal to the predicted value or its upper bound, the system operating cost is the highest, which is more in line with the definition of the "worst case". Therefore, the present invention introduces a binary variable The uncertainty set Ω is rewritten as formula (38).

[0161]

[0162] Therefore, the subproblem (SP) shown in formula (37) can be further rewritten as formula (39):

[0163]

[0164] After the above transformation, the objective function There are still bilinear terms in Therefore, the present invention adopts the big-M method to relax and further linearize The linearization results are as follows:

[0165]

[0166]

[0167] In the formula, is an auxiliary variable used to replace the bilinear term M is a sufficiently large number. Binary state variable When taking 1, When When 0 is taken, Therefore, the subproblem (SP) after linear transformation is further rewritten as formula (43):

[0168]

[0169] Therefore, after the above derivation and transformation, the “max-max-min” IGDT robust optimization problem shown in formula (33) can be decoupled into MP (35) and SP (43) in mixed integer linear form, and the C&CG algorithm embedded in the CPLEX solver is used to iteratively solve the main-subproblem. When the error between the optimal solutions of the main problem is less than the set value through continuous iteration, the adaptability of the system's optimal robust operation strategy to uncertainty under a certain cost deviation factor can be obtained.

[0170] In this embodiment, the tolerance ε of the C&CG algorithm is set to 10 -3, the uncertainty budget Γ is set to 300. Calculate different cost deviation factors The results of the photovoltaic fluctuation deviation ratio ξ under θ are shown in Table 5.

[0171] Table 5 Different The value of ξ under

[0172]

[0173] Figure 4 The worst-case photovoltaic power curve is given. It can be seen that the photovoltaic power takes the predicted value or the lower limit of the corresponding fluctuation range, which conforms to the definition of the worst-case uncertainty concentration in this invention. The simulation was performed over the course of a day. Figure 5 The optimal robust operation results of the system within two hours from 11:00 to 13:00 are given. Figure 5 (a) is the incoming power of the traction substation under the worst case, Figure 5 (b) and (c) are the charge state curves of the battery and supercapacitor under the worst case conditions, respectively. Figure 5 (a) It can be seen that under different cost deviation factors, the worst-case incoming power of the traction substation has a similar trend, but there are certain differences in the specific values. The relevant results are further calculated and summarized in Table 6.

[0174] Table 6. Results of system robust operation under different cost deviations

[0175]

[0176]

[0177] To further analyze the performance of the IGDT robust model, Figure 6 The photovoltaic fluctuation deviation ratio ξ with the cost deviation factor under different photovoltaic configurations is given. The specific values ​​are summarized in Table 7.

[0178] Table 7 Different photovoltaic configurations and The value of ξ under the value

[0179]

[0180] First, it can be seen from the results in Table 5 that decision makers can formulate corresponding robust operation strategies by increasing a certain proportion of budget costs to reduce the impact of photovoltaic uncertainty fluctuations on the stable operation of the system. Increasing the cost by 8% (about 9,600 yuan) can cope with photovoltaic power generation power fluctuations within a range of 19%.

[0181] Secondly, it can be seen from the results in Table 6 that with The increase in demand electricity costs and feed-in electricity remained basically stable. The increase in total power consumption of traction substations increased the electricity cost, but the total operating cost was still within the acceptable range of decision makers and could cope with more photovoltaic uncertainty fluctuations. Figure 5 (b) and (c) show that the slope of SOC represents the charge and discharge rate of each energy storage element under the robust operation strategy. Decision makers can ensure the stable operation of the system by monitoring the operating status of the hybrid energy storage system. In addition, as the cost deviation factor increases, the SOC of the energy storage element changes more frequently, because the energy storage element needs to respond to the wider range of fluctuations in photovoltaic power generation through more frequent output.

[0182] Finally, it can be seen from the results in Table 7 that when the short-circuit capacity of the external grid is certain (500MVA), the larger the photovoltaic configuration capacity, the smaller the photovoltaic power fluctuation range that the system can cope with with the same proportional increase in cost.

[0183] In summary, the day-ahead robust optimization scheduling method for the IGDT-based traction power supply system proposed in the present invention comprehensively and fully considers scheduling decisions, uncertainty set selection and operating cost control. Compared with the traditional traction power supply system, the proposed deterministic day-ahead optimization operation strategy can effectively reduce the operating cost of the traction substation, realize the efficient use of regenerative braking energy, and increase the photovoltaic penetration rate along the railway, so that the system has a certain energy self-sufficiency. Compared with the deterministic model, it can provide decision makers with a second-day operation scheduling plan that takes into account the robustness and economy of the system operation to deal with uncertainty risks. When the uncertainty of the operating environment increases, decision makers can monitor the operating status of the hybrid energy storage system and control the cost budget to ensure the stable operation of the system.

Claims

1. A day-ahead robust optimization scheduling method for a traction power supply system based on IGDT, characterized in that: include: With the goal of minimizing the daily comprehensive operating cost of the traction power supply system, a deterministic day-ahead optimization operation model is established for given PV output and traction load forecast values. Based on the deterministic day-ahead optimization operation model, the IGDT information gap decision theory is introduced to establish an IGDT robust optimization operation model for the day-ahead operation of the traction power supply system, which takes into account scheduling decision, uncertainty set selection and operation cost control. The IGDT robust optimization operation model is solved and the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

2. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 1 is characterized in that: The expression of the deterministic day-ahead optimization operation model is: Among them, min is the minimum function; C day is the daily operating cost of the traction substation; C grid is the electricity cost; C dem is the demand electricity cost; The operation and maintenance cost of the photovoltaic system; The operation and maintenance cost of the energy storage system; is the battery loss cost; N T is the total time period of the day-ahead optimization scheduling cycle; t is the time; m buy The electricity purchase price for the traction substation; The power purchased by the traction substation from the three-phase power grid; m fed The electricity price for feeding into the traction substation; is the power returned from the three-phase power grid by the traction substation; Δt is the scheduling step length in the day-ahead optimization stage; max is the maximum value function; is the demand power; is the maximum demand power; m pv is the operation and maintenance cost price of the photovoltaic system; is the photovoltaic power generation power; m b The operation and maintenance cost price of lithium battery energy storage; is the charging power of the lithium battery energy storage element; is the discharge power of the lithium battery energy storage element; m sc is the operation and maintenance cost price of the supercapacitor; is the charging power of the supercapacitor energy storage element; is the discharge power of the supercapacitor energy storage element; The cost price of lithium battery loss.

3. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 1 is characterized in that: The constraints of the deterministic day-ahead optimization operation model include system power balance constraints, PV constraints, HESS hybrid energy storage system constraints, BTBC constraints and voltage imbalance constraints: in, The power purchased by the traction substation from the three-phase power grid; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; M g is the maximum interactive power between the traction substation and the external power grid; is the return power of the traction substation from the three-phase power grid; max is the maximum value function; is the traction power of the left power supply arm train; It is the traction power of the right power arm train; It is the traction power transmitted to the left supply arm train through the V / v traction transformer; is the direction of power interaction between the left power supply arm of the traction transformer and the back-to-back converter. The power flowing into the left power supply arm of the traction transformer is 1, and the power flowing out of the left power supply arm of the traction transformer is 0; The power returned to the public grid by the left power supply arm; is the braking power of the left power supply arm train; It is the traction power transmitted to the right supply arm train through the V / v traction transformer; is the direction of power interaction between the right power supply arm of the traction transformer and the back-to-back converter. The power flowing into the right power supply arm of the traction transformer is 1, and the power flowing out of the right power supply arm of the traction transformer is 0; The power returned to the public grid by the right power supply arm; The braking power of the right power supply arm train; is the interaction power between the left power supply arm and the α converter; is the interaction power between the α converter and the left power supply arm; is the direction of power interaction between the back-to-back α converter and the traction transformer, the power flowing into the α converter is 1, and the power flowing out of the α converter is 0; is the rated capacity limit of the back-to-back converter; is the interaction power between the right power supply arm and the β converter; is the interaction power between the β converter and the right power supply arm; is the direction of power interaction between the back-to-back β converter and the traction transformer, the power flowing into the β converter is 1, and the power flowing out of the β converter is 0; is the photovoltaic power generation power; P pv,f The upper limit of the photovoltaic output prediction value; is the state of charge of the lithium battery energy storage element at time t; is the state of charge of the lithium battery energy storage element at time t-1; η b,ch The charging efficiency of lithium battery energy storage elements; is the charging power of the lithium battery energy storage element; Δt is the scheduling step length in the day-ahead optimization stage; is the discharge power of the lithium battery energy storage element; η b,dis is the discharge efficiency of the lithium battery energy storage element; is the rated capacity of the lithium battery energy storage element; is the charge state of the supercapacitor energy storage element at time t; is the state of charge of the supercapacitor energy storage element at time t-1; η sc,ch is the charging efficiency of the supercapacitor energy storage element; is the charging power of the supercapacitor energy storage element; is the discharge power of the supercapacitor energy storage element; η sc,dis is the discharge efficiency of the supercapacitor energy storage element; is the rated capacity of the supercapacitor energy storage element; It is the lower limit of the state of charge of the lithium battery energy storage element; It is the upper limit of the state of charge of the lithium battery energy storage element; The state of charge of the lithium battery energy storage element at the beginning; The state of charge of the lithium battery energy storage element at the end of the process; It is the lower limit of the state of charge of the supercapacitor energy storage element; is the upper limit of the state of charge of the supercapacitor energy storage element; is the charge state of the supercapacitor energy storage element at the beginning; is the charge state of the supercapacitor energy storage element at the end of the process; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. is the rated power of the lithium battery; It is a binary state variable. When it is equal to 1, it means that the supercapacitor is in the charging state, and when it is equal to 0, it means that the supercapacitor is in the discharging state. is the rated power of the supercapacitor; a i , b i and c i are the coefficients of the regular dodecagon linearized power flow constraints; is the interactive active power between the left power supply arm of the back-to-back converter and the α converter; is the interactive active power between the α converter and the left power supply arm of the back-to-back converter; It is the interactive active power between the right power supply arm of the back-to-back converter and the β converter; is the interactive active power between the β converter and the right power supply arm of the back-to-back converter; is the reactive power of α converter; is the reactive power of β converter; is the rated capacity of the α converter; is the rated capacity of the β converter; The active power delivered to the left supply arm by the traction transformer; is the active power generated by the α-phase converter; is the active power of the left power supply arm train; The reactive power delivered to the left supply arm by the traction transformer; is the reactive power generated by the α-phase converter; is the reactive power of the left power supply arm train; The active power delivered to the right supply arm by the traction transformer; is the active power generated by the β-phase converter; is the active power of the right power supply arm train; The reactive power delivered to the right supply arm by the traction transformer; is the reactive power generated by the β phase converter; is the reactive power of the right power supply arm train; is the upper limit of voltage imbalance; S d is the short-circuit capacity of the external power grid.

4. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 1 is characterized in that: The expression of the IGDT robust optimization operation model is: stX={Ax≤κ,x∈{0,1}} in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; x is the binary state variable vector in the deterministic day-ahead optimization operation model; X is the feasible domain of x; is the maximization function about x and ξ; u is the uncertainty variable; ξ is the deviation ratio of the uncertainty variable u; is the maximization function with respect to u; is the minimization function about y; y is the continuous variable vector in the deterministic day-ahead optimization operation model; Y(x,u) is the feasible domain of y; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C day is the daily operating cost of the traction substation; C0 is the system operating cost under the deterministic operating environment; A is the coefficient matrix of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; κ is the constant vector of the inequality constraints on the variable vector x in the constraints of the deterministic day-ahead optimization operation model; R is a real number set; E is the coefficient matrix of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; b is the constant vector of the equality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model; K is the inequality constraints on the variable vector y in the constraints of the deterministic day-ahead optimization operation model ; z is the constant vector of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; F is the coefficient matrix of inequality constraints on variable vector x in the constraints of the deterministic day-ahead optimization operation model; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; h is the constant vector of inequality constraints on variable vectors x and y in the constraints of the deterministic day-ahead optimization operation model; J is the coefficient matrix of equality constraints between variable vector y and uncertain variable u in the constraints of the deterministic day-ahead optimization operation model; Ω is the feasible domain of uncertain variable u; is the predicted value of the uncertainty variable u; Γ is the uncertainty budget; is the minimization function about x in a deterministic environment; C is the system operation cost in a deterministic operating environment; P pv,f The upper limit of the photovoltaic output prediction value; is a binary variable representing the power direction of the incoming line of the traction substation. Indicates that the traction substation draws power from the external power grid. Indicates that the traction substation returns electric energy to the external power grid; It is a binary state variable. When it is equal to 1, it means that the lithium battery is in a charging state, and when it is equal to 0, it means that the lithium battery is in a discharging state. It is a binary state variable. When it is equal to 1, it means that the supercapacitor is in the charging state, and when it is equal to 0, it means that the supercapacitor is in the discharging state. The power purchased by the traction substation from the three-phase power grid; It is the return power from the three-phase power grid to the traction substation; It is the traction power transmitted to the left supply arm train through the V / v traction transformer; The power returned to the public grid by the left power supply arm; It is the traction power transmitted to the right supply arm train through the V / v traction transformer; The power returned to the public grid by the right power supply arm; is the interaction power between the left power supply arm and the α converter; is the interaction power between the α converter and the left power supply arm; is the interaction power between the right power supply arm and the β converter; is the interaction power between the β converter and the right power supply arm; is the photovoltaic power generation power; is the charging power of the lithium battery energy storage element; is the discharge power of the lithium battery energy storage element; is the charging power of the supercapacitor energy storage element; is the discharge power of the supercapacitor energy storage element; is the reactive power generated by the α-phase converter; is the reactive power generated by the β phase converter; The reactive power delivered to the left supply arm by the traction transformer; It is the reactive power delivered by the traction transformer to the right supply arm.

5. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 1 is characterized in that: The robust optimization operation model of IGDT is solved to obtain the robust optimization scheduling strategy of the traction power supply system, which is specifically: The IGDT robust optimization operation model is rewritten as a two-stage decision problem; the two-stage decision problem includes a main problem MP and a sub-problem SP; The C&CG algorithm embedded in the CPLEX solver is used to iteratively solve the main-subproblems of the two-stage decision-making problem. When the error between the optimal solutions of the main problem is less than the set value through continuous iteration, the day-ahead robust optimization scheduling strategy of the traction power supply system is obtained.

6. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 5 is characterized in that: The expression of the main problem MP is: in, Robust optimization operation function of IGDT to meet the operation cost budget constraint and robustness requirement; is the cost deviation factor; is the maximization function about x; x is the binary state variable vector in the deterministic optimization scheduling model; X is the feasible domain of x; ξ is the deviation ratio of the uncertainty variable u; η is an auxiliary variable, which represents the actual operating cost in the worst case. The worst case is when the load fluctuation is certain and the photovoltaic output is the smallest in the uncertainty concentration, and the operating cost is the largest; y l is the scheduling decision for each iteration after solving the subproblem; u l is the uncertain variable value under the worst case; C0 is the system operation cost under the deterministic operating environment; c is the objective function minC day The variable coefficient vector of ; min is the minimum function; C day is the daily operating cost of the traction substation; Y(x,u l ) is y l The feasible domain of for u l The feasible domain of is the cost deviation factor in the worst case; l is the scheduling decision and the worst case index; Ψ is the current iteration number.

7. The method for day-ahead robust optimization scheduling of traction power supply system based on IGDT according to claim 5 is characterized in that: The expression of the sub-problem SP is: in, is the bilinear optimization model function of the sub-problem of the day-ahead robust optimization scheduling method for the IGDT-based traction power supply system; x is the binary state variable vector in the deterministic optimization scheduling model; ξ is the deviation ratio of the uncertainty variable u; is the maximization function about u; u is the uncertainty variable; Ω is the feasible domain of the uncertainty variable u; is an auxiliary variable used to replace the bilinear term μ is the dual variable corresponding to the equality constraint of variable vector y; ω is the dual variable corresponding to the inequality constraint of variable vector y; π is the dual variable corresponding to the inequality constraint containing variable vectors x and y; σ is the dual variable corresponding to the equality constraint containing variable vectors y and u; y is the continuous variable vector in the deterministic optimization scheduling model; b is the constant vector of equality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; z is the constant vector of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; h is the constant vector of inequality constraints on variable vectors x and y in the constraints of the deterministic day-ahead optimization operation model; G is the coefficient matrix of inequality constraints on variable vector y in the constraints of the deterministic day-ahead optimization operation model; E is the coefficient matrix of the equality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; K is the coefficient matrix of the inequality constraint on the variable vector y in the constraint conditions of the deterministic day-ahead optimization operation model; F is the coefficient matrix of the inequality constraint on the variable vector x in the constraint conditions of the deterministic day-ahead optimization operation model; J is the coefficient matrix of the equality constraint between the variable vector y and the uncertain variable u in the constraint conditions of the deterministic day-ahead optimization operation model; is a binary auxiliary variable; M is a constant.

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