Calculation method for regulating and controlling operation parameters of bidirectional converter device in real time

Abstract

The invention discloses a calculation method for real-time regulation and control of operation parameters of a bidirectional converter, and the method specifically comprises the steps: enabling a DC traction power supply system to be equivalent to a circuit model, and enabling the bidirectional converter to employ an external characteristic of a sagging oblique line; meanwhile, a traction substation is equivalent to a voltage source and is connected in series with virtual impedance, which is also two groups of optimization variables of the optimization model; a traction contact network and a steel rail are equivalent to parallel impedance, so that an expression of the sum of power of a whole-line traction station is established, minimization is taken as a target function, and operation parameters of the bidirectional converter are optimized and solved; and then decoupling processing is carried out on the two groups of control parameters, each group of parameters is solved respectively, and an original nonlinear and non-convex problem is converted into two linear convex optimization problems, so that real-time regulation and control of the operation parameters of the bidirectional converter in the whole-line traction substation are realized. The method has the advantages of being low in memory requirement, high in calculation speed and the like, and is suitable for energy-saving optimization of the bidirectional converter system and real-time adjustment of control parameters.

Description

Technical Field

[0001] The present invention belongs to the field of rail transit, and in particular relates to a calculation method for real-time regulation of operating parameters of a bidirectional current converter. Background Art

[0002] In urban rail transit systems, coordinated control of bidirectional converters is crucial for precise adjustment of operating parameters. This control mechanism can effectively meet various load requirements by real-time monitoring and dynamic adjustment of key operating parameters such as current and voltage, thereby ensuring that the system achieves optimal performance under different operating conditions. This precise parameter optimization not only significantly improves power supply efficiency, but also effectively reduces energy consumption, thereby enhancing system stability, enabling it to maintain reliable operation under high load or emergency conditions. In addition, coordinated control provides support for the rational allocation of energy and promotes the goal of sustainable development. Therefore, coordinated control and optimization of operating parameters of bidirectional converters are the core factors for improving the energy-saving effect of urban rail transit, and play an important role in promoting the intelligent and environmentally friendly development of urban rail transit in the future.

[0003] However, the current coordinated control of bidirectional converters faces significant challenges, especially the balance between long-term regulation and real-time parameter adjustment. Although long-term parameter regulation can provide a certain degree of system stability, in actual operation, the dynamics of load changes and the external environment make real-time regulation more necessary. Real-time regulation can quickly respond to changes in system status and ensure the immediate optimization of key parameters such as current and voltage, thereby improving power supply efficiency and system safety. If only long-term regulation is relied upon, it may not be able to effectively respond to sudden load changes and fault scenarios, resulting in unstable power supply systems. Therefore, for the coordinated control of bidirectional converters, establishing a real-time regulation mechanism is the key to improving the reliability and efficiency of urban rail transit systems, so as to ensure that they can flexibly respond to various challenges in a complex operating environment. Summary of the invention

[0004] In view of the above situation, the present invention provides a calculation method for real-time control of operating parameters of a bidirectional converter.

[0005] A calculation method for real-time control of operating parameters of a bidirectional converter device of the present invention comprises the following steps:

[0006] Step 1: For the operation of the DC traction power supply system every second, the position and current of the train are obtained in real time. At this time, according to the position of the traction station and the position of the train arrangement, the node Y admittance matrix in the equivalent circuit model of the DC traction power supply system is obtained; at the same time, the node voltage of the traction station in the DC traction power supply system is The current injected into the traction node is The train node voltage is The node voltage of the traction train is The braking train node voltage is The train node injection current is The node injection current of the traction train is The current injected into the braking train node is At this time, the node voltage equation of the DC traction power supply system is shown in formula (1).

[0007]

[0008] where Y TT , Y TV , Y VT , Y VV represents the block matrix of the admittance matrix Y, It is represented by the self-admittance of the traction station nodes and the mutual admittance matrix between the traction station nodes; represents the mutual admittance matrix between the traction depot node and the train node; Represents the mutual admittance matrix between the train node and the traction node, which is equal to Y VT Transpose of a matrix; Represents the self-admittance between train nodes and the mutual-admittance matrix between train nodes.

[0009] Expand the above formula to get:

[0010] I TS =Y TT ·U TS +Y TV ·U V (2)

[0011] I V =Y VT ·U TS +Y VV ·U V (3)

[0012] Combining formula (2) and formula (3), we get:

[0013]

[0014] At the same time, the branch where the traction station model is located should satisfy formula (5):

[0015] I TS =[diag(R TS0 )] -1 ·(U TS0 -U TS )(5)

[0016] in Indicates the virtual impedance of the bidirectional converter of the traction station, represents the working voltage of the bidirectional converter of the traction station. Combining formula (4) and formula (5), the voltage and injection current at the traction station node are obtained:

[0017]

[0018] According to formula (6), the overall power of the DC traction power supply system is expressed as:

[0019]

[0020] Step 2: Establish a real-time optimization model with the minimum overall power of the DC traction power supply system per second as the objective function, the operating parameters of the bidirectional converter as the control variables, and the traction grid voltage as the constraint:

[0021]

[0022] Since the optimization target is a complex nonlinear model with multiple control variables, it is difficult to solve it using common methods; at this time, the optimization model is the working voltage U TS0 and R TS0 The mutually coupled non-convex optimization model chooses to decouple the two control variables. When one control variable is fixed, the optimization model is only related to the other control variable. For a fixed initial control, the separated optimization model solves the single control variable, that is, the objective function is separated into:

[0023]

[0024] For formula (9), the two separated optimization models solve the two control parameters separately by alternating iterative solution method; the convergence judgment condition of the optimization result is:

[0025]

[0026] Wherein ε1 represents the convergence accuracy of the starting voltage of the bidirectional converter of the model, and ε2 represents the convergence accuracy of the virtual impedance of the bidirectional converter of the model.

[0027] The following is a solution for the optimization model of each individual control variable. For formula (9), U is introduced TS0 and R TS0 The mirror variable u TS0 and r TS0 , where the mirror variable is represented as:

[0028]

[0029] Among them, Ω U =[U TS0,min ,UTS0,max ],Ω R =[R TS0,min ,R TS0,max ] is expressed as the range of change of the two controls, and a penalty factor ρ is added to avoid the problem of too large a gap between the control variable and its mirror variable. At this time, the objective function changes to:

[0030]

[0031]

[0032] Then the Lagrangian relaxation factor λ is introduced to form the augmented Lagrangian function:

[0033]

[0034] At this time, the alternating direction multiplier method can be used for optimization, and the control variables of the above formula are alternately optimized:

[0035]

[0036]

[0037] Formulas (14) and (15) are iteratively solved in the order of formulas (16) and (17).

[0038] in They represent the mutual residual and self-residual of the augmented Lagrangian function at the k+1th iteration, which are used to determine the convergence of the algorithm. They are specifically expressed as:

[0039]

[0040] The above formula is iteratively solved in the order of formulas (16) and (17), that is, first fix the mirror variable, Lagrangian relaxation factor, and penalty term, and solve the original control parameter. Then, fix the solved original control parameter, Lagrangian relaxation factor, and penalty term, and solve the mirror variable. Then, fix the solved original control parameter, solved mirror variable, and penalty term, and solve the Lagrangian relaxation factor. Finally, fix the solved original control parameter, solved mirror variable, and Lagrangian relaxation factor, and solve the penalty term. Repeat the above process in sequence until the control parameter meets the convergence accuracy of its corresponding iteration, and then end the iterative solution.

[0041] The solution of the Lagrangian relaxation factor and the penalty term is two simple linear solution processes, while the solution of the original control parameters and mirror variables is still a complex optimization model that requires a formal transformation solution.

[0042] Step 3: Solve the single set of variables U and R in formulas (16) and (17).

[0043] When the train position and injected current are determined every second, its Y admittance matrix becomes a known matrix, where It means that only the system node admittance matrix of the traction station is considered, so the A matrix is ​​a symmetric matrix, and the sum of its row and column elements is 0, that is,

[0044] At this time, for P1=f(U TS0 ), when R TS0 When fixed, formula (7) is expressed as:

[0045]

[0046] Except for the variable U TS0 Except for this, the rest are known quantities. At this time, U TS0 The solution becomes an easy-to-solve quadratic form, namely P1 = U TS0 T QU TS0 +C T U+Z, where Q is a diagonal matrix, C is a column vector, and Z is a constant term; for such a convex optimization model, a nonlinear solver is used to quickly solve it;

[0047] For P2 = f(R TS0 ), when U TS0 When fixed, formula (7) is expressed as:

[0048]

[0049] Except for R TS0 Except for , they are all known quantities. At this time, due to the existence of derivatives of unknown variables, it is still a nonlinear non-convex optimization problem. At this time, auxiliary variables are introduced to process it, and finally expressed as:

[0050]

[0051] At this time, it is converted into an optimization problem that is easy to solve and solved quickly using a nonlinear solver.

[0052] The beneficial technical effects of the present invention are:

[0053] The present invention has the remarkable characteristics of low memory usage and high calculation speed, and is particularly suitable for efficient real-time control of the operating parameters of a bidirectional converter. By combining real-time control and decoupling solution calculation methods, the present invention provides a feasible solution for achieving real-time control of the operating parameters of a bidirectional converter, and is expected to play an important role in improving the system response speed and real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the external characteristics of the bidirectional current conversion device of the present invention.

[0055] Figure 2 It is a schematic diagram of an equivalent circuit model of the urban rail DC traction power supply system of the present invention.

[0056] Figure 3 It is a schematic diagram of an equivalent circuit of a two-station and two-car power supply system of the present invention.

[0057] Figure 4 It is a schematic diagram of the optimized external characteristics of the bidirectional current conversion device of the present invention.

[0058] Figure 5 It is a schematic diagram of decoupling solution of the optimization model of the present invention.

[0059] Figure 6 It is a flow chart of the algorithm for solving the optimization model of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0061] Bidirectional converter adopts Figure 1 The external characteristic model of the constant droop slope, where the slope intersects the Y axis is the starting voltage of the bidirectional converter, and the droop rate is the virtual impedance of the bidirectional converter. Therefore, the bidirectional converter is equivalent to a voltage source in series with a virtual impedance model. The train is equivalent to a constant current source model. The direction of the current source equivalent to the traction train points to the train, and the direction of the current source equivalent to the braking train points to the overhead contact network. Then the overhead contact network and the rail are connected in parallel, which is equivalent to a variable impedance. As the length changes, the equivalent circuit model of the DC traction power supply system is as follows Figure 2 shown.

[0062] by Figure 3 As an example, the equivalent circuit diagram of the two-station and two-car power supply system shown in the figure is used as an example. The two traction stations are equivalent to U TS1 Series R TS1 , U TS2 Series R TS2 , the train is equivalent to I V1 ,I V2 , the DC overhead line and rail are equivalent to R1, R2, R3, R4, and the node voltage of the traction station is U S1 , U S2 , the traction node current is I S1 ,I S2 , the train node voltage is U V1 , U V2 .

[0063] At this time, the node voltage equation in the power supply system is I=Y*U, I=[I S ,I V ] T , I S =[I S1 ,I S2 ] T , I V =[I V1 ,I V2 ] T , U=[U S ,U V ] T , U S =[U S1 ,U S2 ] T , U V =[U V1 ,U V2 ] T , the Y admittance matrix is ​​expressed as:

[0064]

[0065] The overall expression is:

[0066]

[0067] Expanding the above formula, we can get:

[0068]

[0069] For the traction branch, there are:

[0070]

[0071] Combining the above formulas, we can get:

[0072]

[0073] At this time, the sum of the power of the DC traction power supply system is:

[0074]

[0075]

[0076] Based on this, a real-time optimization model of the equivalent circuit was established:

[0077]

[0078] The following is a detailed explanation of the calculation method for quickly solving the port control voltage of the DC traction power supply system.

[0079] Where P is a nonlinear optimization model with two sets of control parameters coupled to each other, such as Figure 4 As shown in the figure, the schematic diagram of the external characteristics of the bidirectional converter is presented. By adjusting the starting voltage and droop rate of the bidirectional converter, the bidirectional converter is decoupled and solved. TS0 The initial value of is [0.06,0.06] T , U TS0 The initial value is [1650,1650] T , so the above equation can be decoupled into

[0080]

[0081] The convergence accuracy is set to ε1=1, ε2=0.001. When the two sets of control parameters meet their convergence accuracy at the same time, the iterative solution ends.

[0082] like Figure 5 As shown, the process of alternating iterative solutions for two sets of control parameters is demonstrated.

[0083] The following solves the optimization model for each individual control variable and introduces U TS0 and R TS0 The mirror variable u TS0 and r TS0 , where the mirror variable is represented as:

[0084]

[0085] Where Ω U =[U TS0,min ,U TS0,max ],Ω R =[R TS0,min ,R TS0,max ] is expressed as the range of change of the two controls, and a penalty factor ρ is added to avoid the problem of too large a gap between the control variable and its mirror variable. At this time, the objective function changes to:

[0086]

[0087] Then, the Lagrangian relaxation factor λ is introduced to form the augmented Lagrangian function:

[0088]

[0089] At this time, the alternating direction multiplier method is used for optimization and solution, and the variables in the above formula are alternately optimized:

[0090]

[0091]

[0092]

[0093] in They represent the mutual residual and self-residual of the augmented Lagrangian function at the k+1th iteration, respectively, and are used to determine the convergence of the algorithm.

[0094] The above formula is iteratively solved in the order of formulas (35) and (36), that is, first fix the mirror variable, Lagrangian relaxation factor, and penalty term, and solve the original control parameter. Then, fix the solved original control parameter, Lagrangian relaxation factor, and penalty term, and solve the mirror variable. Then, fix the solved original control parameter, the solved mirror variable, and penalty term, and solve the Lagrangian relaxation factor. Finally, fix the solved original control parameter, the solved mirror variable, and Lagrangian relaxation factor, and solve the penalty term. Repeat the above process in sequence until the control parameter meets the convergence accuracy of its corresponding iteration, and then end the iterative solution.

[0095] The solution of the Lagrangian relaxation factor and the penalty term is two simple linear solution processes, while the solution of the original control parameters and mirror variables is still a complex optimization model that requires a formal transformation solution.

[0096] The following is the solution of the original control parameters and mirror variables. When the position and injection current of the train are determined every second, its Y admittance matrix becomes a known matrix, where It means that only the system node admittance matrix of the traction station is considered, so the A matrix is ​​a symmetric matrix, and the sum of the elements in each row and column is 0, that is,

[0097] For P1=f(U TS0 ), when R TS0 When fixed, the objective function is expressed as

[0098]

[0099] Except for the variable U TS0 Except for this, the rest are known quantities. At this time, U TS0 The solution becomes an easy-to-solve quadratic form, namely P1 = U TS0 T QU TS0 +C T U+Z, where Q is a diagonal matrix, C is a column vector, and Z is a constant term. Such a convex optimization model can be quickly solved using a nonlinear solver.

[0100] For P2 = f(R TS0 ), when U TS0 When is fixed, the objective function is expressed as:

[0101]

[0102] Except for R TS0 Except for , they are all known quantities. At this time, due to the existence of derivatives of unknown variables, it is still a nonlinear non-convex optimization problem. At this time, auxiliary variables are introduced to process it, and finally expressed as:

[0103]

[0104] At this point, it is converted into an optimization problem that is easy to solve, and can be quickly solved using a nonlinear solver. Figure 6 Flowchart showing the overall optimization solution.

Claims

1. A method for calculating the operating parameters of a bidirectional converter in real time, characterized in that: The following steps are involved: Step 1: For the operation of the DC traction power supply system every second, the position and current of the train are obtained in real time. At this time, according to the position of the traction station and the position of the train arrangement, the node Y admittance matrix in the equivalent circuit model of the DC traction power supply system is obtained; at the same time, the node voltage of the traction station in the DC traction power supply system is The injected current at the traction station node is The train node voltage is The node voltage of the traction train is The braking train node voltage is The train node injection current is The node injection current of the traction train is The current injected into the braking train node is At this time, the node voltage equation of the DC traction power supply system is shown in formula (1): where Y TT , Y TV , Y VT , Y VV represents the block matrix of the admittance matrix Y, It is represented by the self-admittance of the traction station nodes and the mutual admittance matrix between the traction station nodes; Represents the mutual admittance matrix between the traction depot node and the train node; Represents the mutual admittance matrix between the train node and the traction node, which is equal to Y VT Transpose of a matrix; Represents the self-admittance between train nodes and the mutual-admittance matrix between train nodes; Expand the above formula to get: I TS =Y TT ·U TS +Y TV ·U V (2) I V =Y VT ·U TS +Y VV ·U V (3) Combining formula (2) and formula (3), we get: At the same time, the branch where the traction station model is located should satisfy formula (5): I TS =[diag(R TS0 )] -1 ·(U TS0 -U TS )(5) in Indicates the virtual impedance of the bidirectional converter of the traction station, represents the working voltage of the bidirectional converter of the traction station. Combining formula (4) and formula (5), the voltage and injection current at the traction station node are obtained: According to formula (6), the overall power of the DC traction power supply system is expressed as: Step 2: Establish a real-time optimization model with the minimum overall power of the DC traction power supply system per second as the objective function, the operating parameters of the bidirectional converter as the control variables, and the traction grid voltage as the constraint: Since the optimization target is a complex nonlinear model with multiple control variables, it is difficult to solve it using common methods; at this time, the optimization model is the working voltage U TS0 and R TS0 The mutually coupled non-convex optimization model chooses to decouple the two control variables. When one control variable is fixed, the optimization model is only related to the other control variable. For a fixed initial control, the separated optimization model solves the single control variable, that is, the objective function is separated into: For formula (9), the two separated optimization models solve the two control parameters separately by alternating iterative solution method; the convergence judgment condition of the optimization result is: Where ε1 represents the convergence accuracy of the starting voltage of the bidirectional converter of the model, and ε2 represents the convergence accuracy of the virtual impedance of the bidirectional converter of the model; The following is a solution for the optimization model of each individual control variable. For formula (9), U is introduced TS0 and R TS0 The mirror variable u TS0 and r TS0 , where the mirror variable is represented as: Among them, Ω U =[U TS0,min ,U TS0,max ],Ω R =[R TS0,min ,R TS0,max ] is expressed as the range of change of the two controls, and a penalty factor ρ is added to avoid the problem of too large a gap between the control variable and its mirror variable. At this time, the objective function changes to: Then the Lagrangian relaxation factor λ is introduced to form the augmented Lagrangian function: At this time, the alternating direction multiplier method can be used for optimization, and the control variables of the above formula are alternately optimized: Formulas (14) and (15) are iteratively solved in the order of formulas (16) and (17); in They represent the mutual residual and self-residual of the augmented Lagrangian function at the k+1th iteration, which are used to determine the convergence of the algorithm. They are specifically expressed as: Step 3: Solve the single set of variables U and R in formulas (16) and (17); When the train position and injected current are determined every second, its Y admittance matrix becomes a known matrix, where It means that only the system node admittance matrix of the traction station is considered, so the A matrix is ​​a symmetric matrix, and the sum of its row and column elements is 0, that is, At this time, for P1=f(U TS0 ), when R TS0 When fixed, formula (7) is expressed as: Except for the variable U TS0 Except for this, the rest are known quantities. At this time, U TS0 The solution becomes an easy-to-solve quadratic form, namely P1 = U TS0 T QU TS0 +C T U+Z, where Q is a diagonal matrix, C is a column vector, and Z is a constant term; for such a convex optimization model, a nonlinear solver is used to quickly solve it; For P2 = f(R TS0 ), when U TS0 When fixed, formula (7) is expressed as: Except for R TS0 Except for , they are all known quantities. At this time, due to the existence of derivatives of unknown variables, it is still a nonlinear non-convex optimization problem. At this time, auxiliary variables are introduced to process it, and finally expressed as: At this time, it is converted into an optimization problem that is easy to solve and solved quickly using a nonlinear solver.

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