RPC traction power supply harmonic suppression method based on robust H-infinity control

Abstract

The invention discloses a RPC traction power supply harmonic suppression method based on robust H-infinity control, and relates to the technical field of high-speed railway electric power, and the method comprises the steps: analyzing the electric energy quality of a railway traction power supply system; constructing a vehicle-network coupled traction power supply system module engineering model; building a quadruple RPC model based on robust H infinity control; and constructing a locomotive simulation model and designing a six-working-condition parallel APF model to carry out electric energy quality analysis. According to the RPC traction power supply harmonic suppression method based on robust H-infinity control provided by the invention, harmonic suppression is carried out on the traction network by applying the RPC based on robust H-infinity control, so that the operation safety of the electrified railway is promoted to be improved, and a real solution is provided for further enhancing the reliable operation of the electrified railway traction power supply system.

Description

Technical Field

[0001] The invention relates to the technical field of high-speed railway electric power, and in particular to a method for suppressing harmonics in traction power supply based on robust H∞ control (RPC). Background Art

[0002] The traction power supply system plays a vital role in high-speed railways and is a key subsystem to ensure the safe operation of high-speed railways. Once the power supply arms on both sides of the traction substation are in different operating conditions, the balance of the system will be broken, posing a great threat to railway transportation safety. Therefore, it is of great significance to conduct an in-depth analysis of high-frequency resonance characteristics and develop effective suppression methods.

[0003] Nowadays, there are many studies in the field of harmonic control. Although some progress has been made in the suppression of low-order harmonics, high-order harmonics still exist. It can be seen that exploring the harmonic generation mechanism and current harmonic characteristics of EMUs under various working conditions is the core point to solve the harmonic problem of high-speed railways. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is that the existing harmonic control methods have poor safety.

[0006] Low reliability, easy to cause harmonic problems, and the problem of high-order harmonics still exists.

[0007] To solve the above technical problems, the present invention provides the following technical solutions: a method for suppressing harmonics in traction power supply based on robust H∞ control RPC, comprising analyzing the power quality of the railway traction power supply system; constructing a module engineering model of the traction power supply system coupled with the vehicle grid; building a quadruple RPC model based on robust H∞ control; constructing a locomotive simulation model and designing six types of parallel APF models for power quality analysis.

[0008] As a preferred solution of the method for harmonic suppression of RPC traction power supply based on robust H∞ control described in the present invention, wherein: the analysis of the power quality of the railway traction power supply system includes a parallel quadruple topology structure. Since the topology of each RPC is consistent and the α power supply arm is symmetrical with the β power supply arm, only a single-side VSC equivalent circuit model is displayed;

[0009] u c is the equivalent voltage of VSC AC side, u T is the AC voltage of the traction network, u s is the AC voltage on the low voltage side, i is the current flowing through the AC side of the VSC, i dc is the current flowing through the DC side of the VSC;

[0010] The equivalent voltage u on the AC side of the VSC c is expressed as:

[0011]

[0012] where u c is the equivalent voltage on the AC side of the VSC, λ represents the PWM modulation depth of the VSC, k c is the amplitude adjustment coefficient of the voltage u c , ω is the angular frequency, and δ represents the phase angle of the inverter output relative to u s ;

[0013] The circuit equations of the AC side and DC side of the VSC are expressed as:

[0014]

[0015] where u s is the AC voltage on the low-voltage side, and C is the capacitor;

[0016] The steady-state mathematical model of the single-side VSC of the RPC is expressed as:

[0017]

[0018] where i d and i q are the dq components of the current i, and U s represents the effective value of the reference phasor u s ;

[0019] As a preferred solution of the method for suppressing traction power supply harmonics based on robust H∞ control for the RPC described in the present invention, wherein: the construction of the engineering model of the traction power supply system module with vehicle-network coupling includes that the RPC module is controlled by a voltage-current double closed-loop, and the control strategy adopted by the RPC amplitude-phase control is the control method of LMI based on robust H∞ control;

[0020] The state equation of the system is expressed as:

[0021]

[0022] where u is the control input, d is the disturbance, x = [x 1 x 2 T , x 1 , x 2 represent state variables; the matrix A represents the system matrix, indicating the relationship between the internal state variables of the system; the matrix B represents the input matrix, indicating the influence of the input on the system state;

[0023] The controller equation is expressed as:

[0024] ​U = Kx

[0025] where the controller gain matrix K = [k 1 k 2 , k 1 and k 2 are controller parameters;

[0026] The control objective is to achieve x → 0 by designing and solving the LMI;

[0027] H∞ control aims to minimize the norm of the transfer function from the disturbance input to the system output.

[0028] As a preferred embodiment of the robust H∞ control RPC traction power supply harmonic suppression method described in the present invention, wherein: the construction of the vehicle-network coupled traction power supply system module engineering model includes an H∞ controller including:

[0029] Design the Lyapunov function:

[0030] V = x T Px

[0031] where P is a positive definite matrix;

[0032] Take the derivative of V:

[0033]

[0034] Rearrange:

[0035]

[0036] where Q is an intermediate derivation matrix, Q = [P(A + BK)] T + P(A + BK); η = [x T d T T , and η is a vector composed of the system state and the disturbance;

[0037] Set the output:

[0038]

[0039] The output needs to meet the performance index:

[0040]

[0041] where γ is a performance index correlation coefficient, and γ > 0;

[0042] Stability judgment, by constructing a matrix:

[0043]

[0044] ​Analyze the stability of the system and output the convergence result of the system state x:

[0045]

[0046] where v max represents the upper bound of the disturbance energy, V(0) is the initial value of the Lyapunov function, and P min is the minimum eigenvalue of the positive definite symmetric matrix;

[0047] The LMI design is expressed as:

[0048] Let F = KP -1 , N = P -1 , then P -1 K T = F T , then output the first LMI:

[0049]

[0050] Output another LMI according to the definition of P:

[0051] N > 0, N = N T .

[0052] As a preferred solution of the RPC traction power supply harmonic suppression method based on robust H∞ control according to the present invention, wherein: the construction of the quadruple RPC model based on robust H∞ control includes a energy storage device including a lithium battery energy storage part, and the PNGV model is selected;

[0053] The lithium battery has two states of charging and discharging. When the battery is in the discharging state, the load current i bat > 0, R d , V a , V g are respectively:

[0054]

[0055] When the battery is in the charging state, the load current i bat < 0, R d , V a , V g are respectively:

[0056]

[0057] where the variables S b and S g are expressed as:

[0058]

[0059] where V gIndicates the tail rise of the charging voltage, V a Indicates the maximum saturation voltage drop, R d Indicates the internal resistance of the battery during discharge, V a0 Indicates V a Constant value, V a1 Indicates V a Coefficient of variation, SOC represents the state of charge of the current, S a Indicates the influence of SOC on V a Influence point of, S b Is the influence of SOC on V g Influence point of, R 0 Indicates the internal resistance constant value, R 1 Indicates the internal resistance variation coefficient, S d Indicates the threshold state of charge, i bat Indicates the battery current, R c Indicates the charging internal resistance, V ga Indicates the charging voltage coefficient.

[0060] As a preferred embodiment of the method for suppressing harmonic waves in RPC traction power supply based on robust H∞ control according to the present invention, wherein: the construction of the locomotive simulation model and the design of the parallel-type APF model under six working conditions for power quality analysis include a parallel-type APF, which cancels the harmonic current in the power grid by generating a current source;

[0061] For the selection of the DC-side voltage of the main circuit of the APF, the DC-side voltage U of the main circuit of the APF dc Affects the compensation ability for harmonics;

[0062] Outputs the DC-side voltage according to the harmonic frequency and amplitude to be compensated, and the capacity of the device;

[0063] U dc Take the peak value at the connection point of the APF and the coupling transformer:

[0064]

[0065] Among them, k is the transformation ratio coefficient of the coupling transformer.

[0066] As a preferred embodiment of the method for suppressing harmonic waves in RPC traction power supply based on robust H∞ control according to the present invention, the construction of the locomotive simulation model and the design of the parallel-type APF model under six working conditions for power quality analysis include the selection of the DC-side capacitor of the main circuit. Since the DC-side capacitor of the active filter is always in the charge and discharge state during normal operation, assuming that the capacitor is always in the charge or discharge state within one cycle, the maximum allowable deviation of the output DC-side capacitor voltage from the set value is ΔU dcmax , The DC-side capacitor of the main circuit of the APF is:

[0067]

[0068] Where C is the DC side capacitance value; PWM is the pulse frequency; is the maximum current passing through the capacitor.

[0069] Another object of the present invention is to provide a traction power supply harmonic suppression system based on robust H∞ control RPC, which can solve the problem that the current harmonic control method contains easily induced harmonics and negative sequence problems by building a quadruple RPC model based on robust H∞ control.

[0070] As a preferred solution of the RPC traction power supply harmonic suppression system based on robust H∞ control described in the present invention, it includes: an initialization module, an RPC model construction module, a locomotive simulation model construction module, and a locomotive operating condition design module; the initialization module is used to analyze the power quality problems of the railway traction power supply system; the RPC model construction module is used to construct a module engineering model of the vehicle-grid coupled traction power supply system, and build a quadruple RPC model based on robust H∞ control; the locomotive operating condition design module is used to construct a locomotive simulation model and design six operating conditions.

[0071] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a method for suppressing traction power supply harmonics based on robust H∞ control (RPC).

[0072] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for suppressing traction power supply harmonics based on robust H∞ control (RPC).

[0073] Advantages of the present invention: The method for suppressing harmonic in RPC traction power supply based on robust H∞ control provided by the present invention has a quadruple topology structure, which is more complex. It is crucial to maintain the stability of the system. LMI control can analyze the stability of the system by constructing an appropriate Lyapunov function. The LMI control algorithm can effectively control the system state by using the system matrix and the controller gain matrix. The controller design based on the H∞ index can optimize the performance of the RPC system. In the RPC system, set the output Z = Cx, construct a matrix through the set performance index to judge the stability of the system, and optimize the controller design to make the harmonic suppression effect of the system reach the optimal. By adjusting the controller parameters, reduce the influence of harmonics on the motor performance index, and ensure the compensation accuracy, so as to enhance the robustness and stability of the whole system. The combination of LMI and H∞ control theory can take multiple performance indexes into consideration by constructing a rigorous control system, design an efficient controller, and accurately deal with the complex power problems encountered by the quadruple RPC to ensure the stable operation of the system. APF has unique advantages in harmonic control. It can accurately detect and quickly generate a compensation current with the same magnitude and opposite direction as the harmonic current to effectively cancel the harmonics. When working in coordination with the quadruple RPC, under the overall coordination of the combination of LMI and H∞ control theory, the two form a powerful force, which can comprehensively optimize the power quality of the power system, build a solid foundation for scenarios with high requirements for power quality such as traction power supply systems, and ensure the efficiency and reliability of power supply. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0075] Figure 1 FIG. is a schematic flow chart of a method for suppressing harmonic in RPC traction power supply based on robust H∞ control provided by the first embodiment of the present invention.

[0076] Figure 2 FIG. is an equivalent circuit model diagram of a method for suppressing harmonic in RPC traction power supply based on robust H∞ control provided by the first embodiment of the present invention.

[0077] Figure 3 FIG. is an equivalent circuit diagram of a train of a method for suppressing harmonic in RPC traction power supply based on robust H∞ control provided by the first embodiment of the present invention.

[0078] Figure 4The equivalent circuit diagram of an APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the first embodiment of the present invention.

[0079] Figure 5 The traction network side voltage waveform diagrams of the α-side and β-side with one locomotive each after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0080] Figure 6 The grid side current waveform diagrams of the α-side and β-side with one locomotive each after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0081] Figure 7 The 1-100th order current harmonic diagrams of the α and β traction network sides at working condition 2 for the α-side and β-side with one locomotive each after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0082] Figure 8 The 1-100th order harmonic diagrams of the traction network side current harmonic components under six working conditions for the α-side and β-side with one locomotive each after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0083] Figure 9 The comparison diagrams of the 1-100th order harmonic components of the traction network side current before and after filtering by RPC and APF under four working conditions of working condition 1, 2, 3, and 4 when there is one locomotive on each of the α-side and β-side for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0084] Figure 10 The 1-100th order harmonic diagrams of the traction network side current harmonic components under six working conditions for the α-side and β-side with two locomotives each after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0085] Figure 11 The comparison diagrams of the 1-100th order harmonic components of the traction network side current before and after filtering by RPC and APF for a harmonic suppression method of RPC traction power supply based on robust H∞ control provided for the second embodiment of the present invention.

[0086] Figure 12For a harmonic suppression method of RPC traction power supply based on robust H∞ control provided in the second embodiment of the present invention, the comparison diagrams of the current harmonic components of the traction network side with one locomotive and two locomotives on each of the α side and the β side after RPC and APF filtering are selected for four working conditions, namely working conditions 1, 2, 3, and 4, for the 1st to 100th harmonics.

[0087] Figure 13 For a harmonic suppression method of RPC traction power supply based on robust H∞ control provided in the second embodiment of the present invention, the high-order harmonic diagrams of the current harmonic components of the traction network side with two locomotives on each of the α side and the β side after RPC and APF filtering are shown for six working conditions, for the 400th to 500th harmonics.

[0088] Figure 14 For a harmonic suppression method of RPC traction power supply based on robust H∞ control provided in the first embodiment of the present invention, when there are two locomotives on each of the α side and the β side, the comparison diagrams of the harmonic waveforms of the current harmonic components of the traction network side before filtering with one locomotive on each of the α side and the β side after RPC and APF filtering are selected for two working conditions, namely working conditions 1 and 2, for the 400th to 500th harmonics. Detailed implementation manners

[0089] To make the above objects, features, and advantages of the present invention more apparent and understandable, the following will describe the detailed implementation manners of the present invention in conjunction with the accompanying drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0090] Embodiment 1, referring to Figure 1 - Figure 4 , which is an embodiment of the present invention, provides a harmonic suppression method of RPC traction power supply based on robust H∞ control, including:

[0091] S1: Analyze the power quality of the railway traction power supply system.

[0092] Furthermore, the present invention realizes the governance of power quality through devices such as RPC with a parallel multiplications topology to ensure the safe and reliable operation of the train, and at the same time improve the efficiency and stability of the power supply system. The equivalent circuit model of the RPC single-side VSC (voltage source converter) is as follows Figure 2 shown.

[0093] Among them, u c is the equivalent voltage on the AC side of the VSC, u T is the AC voltage of the traction network, u s is the AC voltage on the low-voltage side, i is the current flowing through the AC side of the VSC, and i dc is the current flowing through the DC side of the VSC.

[0094] Among them, the equivalent AC-side voltage u of the VSC c The expression is as follows:

[0095]

[0096] λ represents the PWM (pulse width modulation) modulation depth of the VSC, and k c is the amplitude adjustment coefficient of the voltage u c ω is the angular frequency, and δ represents the phase angle of the inverter output relative to u s .

[0097] The circuit equation expressions of the AC side and DC side of the VSC are respectively:

[0098]

[0099] From Figure 3 Comprehensively, the steady-state mathematical model of the RPC single-side VSC (voltage source converter) is:

[0100]

[0101] Among them, i d and i q are the dq components of the current i, and U s represents the effective value of the reference phasor u s .

[0102] S2: Construct the engineering model of the vehicle-grid coupled traction power supply system module.

[0103] Furthermore, in the actual control system, there are often some inevitable interference factors, which are called disturbances. These disturbances will interfere with the performance indicators such as the stability and robustness of the system. In this patent, the RPC module adopts voltage-current double closed-loop control. In order to meet the stability and robustness of the system, the control strategy adopted by the RPC amplitude-phase control is the LMI control method based on robust H∞ control.

[0104] The state equation of the system is:

[0105]

[0106] Among them, u is the control input, d is the disturbance, and x = [x 1 x 2 T , x 1 , x 2 represent state variables; the matrix A represents the system matrix, indicating the relationship between the internal state variables of the system; the matrix B represents the input matrix, indicating the influence of the input on the system state. ​

[0107] The controller equation is as follows:

[0108] U = Kx

[0109] where the controller gain matrix K = [k 1 k 2 , and k 1 , k 2 are controller parameters;

[0110] The control objective is to achieve x → 0 by designing LMI solutions. That is, regardless of the disturbances the system is subjected to, by designing an appropriate controller, the state of the system will ultimately tend to zero, ensuring the stability of the system.

[0111] H∞ control aims to minimize the norm of the transfer function from the disturbance input to the system output (which can be the system state in this case). Simply put, it is to minimize the output energy of the system under the worst disturbance conditions, thereby ensuring the robustness and stability of the system in the presence of disturbances.

[0112] The design of the H∞ controller is as follows:

[0113] Design the Lyapunov function:

[0114] V = x T Px

[0115] where P is a positive definite matrix (P > 0 and P = P T ).

[0116] Taking the derivative of V gives:

[0117]

[0118] Substituting and simplifying gives:

[0119]

[0120] where Q is an intermediate derivation matrix, Q = [P(A + BK)] T + P(A + BK); η = [x T d T T , and η is a vector composed of the system state and the disturbance.

[0121] Set the output:

[0122]

[0123] The output needs to meet the performance index:

[0124]

[0125] ​Among them, γ is the correlation coefficient of the performance index, and γ > 0.

[0126] Stability judgment: By constructing the matrix:

[0127]

[0128] to analyze the stability of the system, and finally obtain the convergence result of the system state x:

[0129]

[0130] Among them, v max represents the upper bound of the disturbance energy, V(0) is the initial value of the Lyapunov function, and P min is the minimum eigenvalue of the positive definite symmetric matrix.

[0131] LMI design is as follows:

[0132] Let F = KP -1 , N = P -1 , then P -1 K T = F T , then the first LMI can be obtained:

[0133]

[0134] Another LMI can be deduced from the definition of P:

[0135] N > 0, N = N T .

[0136] S3: Build a quadruple RPC model based on robust H∞ control.

[0137] Furthermore, the energy storage device includes a lithium battery energy storage part. To ensure the accuracy of the battery model and simplify the model structure, this patent selects the PNGV model. The PNGV model adds a series capacitor on the basis of the Thevenin equivalent model, which can better simulate the dynamic characteristics of the lithium battery.

[0138] The lithium battery includes two states: charging and discharging. When the battery is in the discharging state, the load current i bat > 0, R d , V a , V g are respectively:

[0139]

[0140] When the battery is in the charging state, the load current i bat < 0, R d , V a , V g are respectively:

[0141]

[0142] Among them, the variable S b and S g are expressed as:

[0143]

[0144] Among them, V g represents the tail rise of the charging voltage, V a represents the maximum saturation voltage drop, R d represents the internal resistance of the battery during discharge, V a0 represents V a constant value, V a1 represents V a variation coefficient, SOC represents the state of charge of the current, S a represents the influence point of SOC on V a , S b is the influence point of SOC on V g , R 0 represents the internal resistance constant value, R 1 represents the internal resistance variation coefficient, S d represents the threshold state of charge, i bat represents the battery current, R c represents the charging internal resistance, V ga represents the charging voltage coefficient.

[0145] S4: Construct a locomotive simulation model and design a six - working - condition shunt - type APF model for power quality analysis.

[0146] Furthermore, the shunt - type APF (active power filter) is equivalent to a harmonic current generator with an inverter. By generating a current source, this current source cancels out the harmonic current in the power grid, thereby achieving the effect of filtering harmonics.

[0147] Regarding the selection of the DC - side voltage of the main circuit of the APF, since the magnitude of the DC - side voltage U dc of the main circuit of the APF will affect its harmonic compensation ability. Usually, it is necessary to calculate the appropriate DC - side voltage according to factors such as the harmonic frequency and amplitude to be compensated, and the capacity of the device. Generally, the magnitude of U dc is taken as the peak value at the connection point of the APF and the coupling transformer. In this patent, it is selected as:

[0148]

[0149] Among them, k is the turns - ratio coefficient of the coupling transformer.

[0150] For the selection of the DC-side capacitor of the main circuit, since the DC-side capacitor of the active power filter is always in the charging and discharging state during normal operation, assuming that the capacitor is always in the charging or discharging state within a certain period, the maximum allowable deviation of the DC-side capacitor voltage from the set value can be obtained as, and thus the DC-side capacitor of the APF main circuit can be obtained as:

[0151]

[0152] where C is the value of the DC-side capacitor; PWM is the pulse frequency; is the maximum current value passing through the capacitor.

[0153] It should be noted that in the railway power supply system, the traction transformer, as the core hub for energy conversion in the traction power supply system, needs to convert the three-phase alternating current transmitted by the power system into the single-phase alternating current required for traction equipment such as EMUs to operate. Converting the three-phase alternating current into a single-phase alternating current enables the electric energy to be transmitted to the EMU in a suitable form. The selected V / v connection method consists of two single-phase transformers. The primary windings are respectively connected to two phases of the three-phase power system, such as phase A and phase B, to obtain the grid line voltage. The two sides of the secondary winding are respectively connected to the two phases α and β of the supply arm. There are electric locomotives running under the two supply arms. The grid electric energy in the system is supplied to the locomotive through the pantograph, supporting the energy required for the locomotive operation. The supplied current then returns to the transformer through the rail. The voltage of the primary winding is the line voltage. For a three-phase 110 kV or 220 kV system, the line voltage is times the phase voltage. The simulation parameters of the traction power supply system are shown in Table 1.

[0154] Table 1 Simulation parameters of the traction power supply system

[0155] System parameters Value Three-phase system voltage / kV 220 Capacity of traction substation / MW 40 Transformer turns ratio of traction substation 220:27.5 Capacity of AT substation MW 40 Simulation duration / s 0.3

[0156] The left supply arm is phase α, and the right is phase β. The voltages of the two arms are:

[0157]

[0158] u A 、u B 、u C are the three-phase grid voltages, and k is the transformer turns ratio. Further, the three-phase AC currents on the grid side can be obtained according to the load of the supply arm:

[0159]

[0160] As the RPC traction power supply harmonic suppression scheme based on the robust H∞ control LMI algorithm of the present invention, wherein: the present invention realizes the governance of power quality such as harmonics through the RPC with a parallel multiplexing structure. The RPC is connected in parallel to the traction power supply system, and each RPC unit contains key converter components inside. The converter, as the core hub for power conversion and regulation, performs real-time control on electrical quantities such as current and voltage according to precise control strategies.

[0161] The steady-state mathematical model of the RPC single-sided VSC (voltage source converter) is:

[0162]

[0163] In an actual control system, there are often some inevitable interference factors, which are called disturbances. These disturbances will interfere with performance indicators such as the stability and robustness of the system. The RPC module described in this patent uses a double closed-loop of voltage and current for control. In order to meet the stability and robustness of the system, the control strategy adopted for the RPC amplitude-phase control is the control method based on the LMI of robust H∞ control.

[0164] The state equation of the system is:

[0165]

[0166] Among them, u is the control input, d is the disturbance, and x = [x 1 x 2 T ,x 1 、x 2 represent state variables; the matrix A represents the system matrix, indicating the relationship between the internal state variables of the system; the matrix B represents the input matrix, indicating the influence of the input on the system state.

[0167] The controller equation is:

[0168] U = Kx

[0169] Among them, the controller gain matrix K = [k 1 k 2 , k 1 、k 2 are controller parameters;

[0170] The control objective is to achieve x → 0 by designing the LMI solution. That is, no matter what kind of disturbance the system is subjected to, by designing a suitable controller, the state of the system will eventually tend to zero, ensuring the stability of the system.

[0171] ​H∞ control aims to minimize the norm of the transfer function from the disturbance input to the system output (which can be the system state in this case). Simply put, it minimizes the output energy of the system under the worst disturbance conditions, thus ensuring the robustness and stability of the system in the presence of disturbances.

[0172] The design of the H∞ controller is as follows:

[0173] Design the Lyapunov function:

[0174] V = x T Px

[0175] where P is a positive definite matrix (P > 0 and P = P T ).

[0176] Taking the derivative of V gives:

[0177]

[0178] Substituting and simplifying gives:

[0179]

[0180] where Q is an intermediate derivation matrix, Q = [P(A + BK)] T + P(A + BK); η = [x T d T T , and η is a vector composed of the system state and the disturbance.

[0181] Set the output:

[0182]

[0183] The output needs to satisfy the performance index:

[0184]

[0185] where γ is the performance index correlation coefficient, and γ > 0.

[0186] Stability judgment: By constructing the matrix:

[0187]

[0188] to analyze the stability of the system, and finally obtain the convergence result of the system state x:

[0189]

[0190] where, v max represents the upper bound of the disturbance energy, V(0) is the initial value of the Lyapunov function, P min ​is the minimum eigenvalue of a positive definite symmetric matrix.

[0191] The LMI design is as follows:

[0192] Let F = KP -1 , N = P -1 , then P -1 K T = F T , then the first LMI can be obtained:

[0193]

[0194] Another LMI can be deduced from the definition of P:

[0195] N > 0, N = N T

[0196] In the lithium battery energy storage part, in order to ensure the accuracy of the battery model and simplify the model structure, this patent selects the PNGV model (adding a series capacitor on the basis of the Thevenin equivalent model), which can better simulate the dynamic characteristics of the lithium battery.

[0197] The lithium battery includes two states: charging and discharging. When the battery is in the discharging state, the load current i bat > 0, R d , V a , V g are respectively:

[0198]

[0199] When the battery is in the charging state, the load current i bat < 0, R d , V a , V g are respectively:

[0200]

[0201] Among them, the variables S b and S g are expressed as:

[0202]

[0203] The main circuit of the train can be simplified to a three-level four-quadrant main circuit and can be simplified with an equivalent model. Its equation is:

[0204]

[0205] is the voltage phasor on the low-voltage side, is the fundamental current phasor on the low-voltage side, is the fundamental phasor of the PWM modulation voltage. The control mode of the multiple unit train is PWM control. By performing double closed-loop PI control on the amplitude to adjust the phase, the fundamental power factor on the AC side can meet the standard. The modulation wave has an amplitude affected by phase adjustment, which can keep the power supply on the intermediate DC side at a stable level.

[0206] Combined with the locomotive model and the traction power supply system, six types of locomotive operating conditions are designed to conduct negative sequence and harmonic analysis on the grid side. Refer to Table 2.

[0207] Table 2 Explanation of Six Types of Operating Conditions

[0208]

[0209] Furthermore, in the case of multiple operating conditions, an adaptive experiment is carried out on the parameters of the shunt APF filter, and the harmonic characteristics of the traction power supply system under multiple operating conditions are studied. The parameters of the APF main circuit are set as shown in Table 3. The output inductor L of the APF main circuit f = 0.05 H, the DC side capacitor C = 0.025 F, and the capacitor voltage

[0210] Table 3 Parameter Table of APF Main Circuit

[0211]

[0212] Example 2, referring to Figure 5 - Figure 14 , is an embodiment of the present invention, which provides a method for suppressing harmonic waves in RPC traction power supply based on robust H∞ control. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiment.

[0213] First, in the case of multiple operating conditions, when there is one vehicle on each of the α power supply arm and the β power supply arm, an adaptive experiment is carried out on the parameters of the RPC traction power supply harmonic suppression scheme based on the LMI algorithm of robust H∞ control. Set the simulation time as shown in Table 2, and extract FFT harmonic data.

[0214] In order to simulate more complex operating conditions, when there are two vehicles running in parallel on each of the α power supply arm and the β power supply arm, and repeating the above experiment, Table 4 can be obtained:

[0215] Table 4 Harmonic Characteristic Comparison Table

[0216]

[0217] Combined with Table 4, it can be seen that the current THD values under different working conditions are different. When the left power supply arm is in the braking condition, the THD value of the current is significantly larger, while when the left power supply arm is in the traction condition, it is significantly smaller. Compared with before filtering, the THD value of the filtered current is significantly smaller, and the filtering effect is obvious. Compared with more complex working conditions, the current THD value when four locomotives are running in parallel varies more than when two locomotives are running in parallel, sometimes larger and sometimes smaller, but the differences are not significant. Considering the actual operation is more complex, this is a reasonable situation. However, the current THD values in both cases are significantly smaller than before filtering, the filtering effect is remarkable, and it meets the experimental expectations.

[0218] Figure 5 These are the traction network side voltage waveforms of one locomotive on each of the α side and β side after RPC and APF filtering of the present invention, showing the traction network side voltage waveforms of the present invention from 0s to 2s. The voltage fluctuates up and down when the locomotive working condition changes, and the widest width of the waveform fluctuation is about ±2.4×10 4 V.

[0219] Figure 6 These are the grid side current waveform diagrams of one locomotive on each of the α side and β side after RPC and APF filtering of the present invention, showing the grid side current harmonics of the present invention from 0s to 2s. The three-phase current fluctuates up and down when the locomotive working condition changes.

[0220] Figure 7 These are the 1 - 100th order current harmonic diagrams of the α and β traction network sides of one locomotive on each of the α side and β side after RPC and APF filtering of the present invention under working condition 2. It can be seen that the α side is slightly lower than the β side at the 50th and 95th harmonics.

[0221] Figure 8 These are the 1 - 100th order harmonic diagrams of the traction network side current harmonic components of one locomotive on each of the α side and β side after RPC and APF filtering of the present invention under six working conditions. It can be seen from the figure that the high-order harmonics are also mainly distributed near the 25th, 50th, and 95th harmonics.

[0222] Figure 9 These are the comparison diagrams of the 1 - 100th order harmonic components of the traction network side current before and after RPC and APF filtering under four working conditions of working condition 1, 2, 3, and 4 when there is one locomotive on each of the α side and β side of the present invention. It can be seen that after RPC and APF filtering, the traction network current harmonics decrease significantly at low harmonics and near the 50th and 95th harmonics.

[0223] Figure 10These are the harmonic component diagrams of the 1st - 100th order traction network side current under six working conditions with two locomotives on each of the α - side and β - side after RPC and APF filtering in the present invention. It can be seen from the figure that the high - order harmonics are mainly distributed around the 25th, 50th, and 95th harmonics.

[0224] Figure 11 When there are two locomotives on each of the α - side and β - side in the present invention, these are the comparison diagrams of the 1st - 100th order harmonic components of the traction network side current before and after RPC and APF filtering for four working conditions, namely condition 1, condition 2, condition 3, and condition 4. It can be seen that after RPC and APF filtering, the harmonic components of the traction network current significantly decrease in the low - order harmonics, around the 50th, and 95th harmonics.

[0225] Figure 12 These are the comparison diagrams of the 1st - 100th order harmonic components of the traction network side current with one locomotive and two locomotives on each of the α - side and β - side after RPC and APF filtering for four working conditions, namely condition 1, condition 2, condition 3, and condition 4 in the present invention. It can be seen that around the 25th harmonic, the current harmonic waveforms of two locomotives on each of the α - side and β - side significantly decrease.

[0226] Figure 13 These are the waveforms of the 400th - 500th order high - order harmonic components of the traction network side current under six working conditions with two locomotives on each of the α - side and β - side after RPC and APF filtering in the present invention. It can be seen from the figure that the harmonic content increases with the increase of the harmonic order under different working conditions, but the increasing amplitude and fluctuation vary with the working conditions. Among them, the harmonic content is relatively low under the working condition of α - side traction and β - side braking, while the harmonic content is relatively high under the working condition of α - side braking and no vehicle on the β - side.

[0227] Figure 14 When there are two locomotives on each of the α - side and β - side in the present invention, these are the comparison diagrams of the waveforms of the 400th - 500th order harmonic components of the traction network side current after RPC and APF filtering for two working conditions, namely condition 1 and condition 2, and before filtering with one locomotive on each of the α - side and β - side. It can be seen from the figure that before filtering, the harmonic content of condition 1 and condition 2 fluctuates greatly and the values are relatively high; after filtering, the harmonics of condition 1 and condition 2 are obvious as a whole, which indicates that the filtering measures have a significant effect on reducing the harmonic content.

[0228] Example 3, an embodiment of the present invention, provides a harmonic suppression system for RPC traction power supply based on robust H∞ control, including an initialization module, a parallel - type active power filter construction module, a simulation module of the vehicle - network - coupled traction power supply system, a locomotive working condition design module, and a harmonic characteristic and negative - sequence analysis module.

[0229] Among them, the initialization module is used to analyze the harmonic problems of the high-speed railway traction power supply system. The shunt active power filter construction module is used to construct a shunt active power filter using the PPF harmonic control solution. The simulation module of the vehicle-network coupled traction power supply system is used to establish a simulation model of the vehicle-network coupled traction power supply system in combination with actual data. The locomotive operating condition design module is used to set parameters for the traction power supply system simulation model and design six locomotive operating conditions. The harmonic characteristics and negative sequence analysis module is used to conduct adaptive experiments on the parameters of the shunt APF filter and analyze the harmonic characteristics and negative sequence of the traction power supply system under multiple operating conditions.

[0230] If the functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods in various embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs, etc., which can store program codes.

[0231] The logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device.

[0232] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection (electronic device) having one or more wirings, a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable media can even be paper or other suitable media on which a program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or, if necessary, other suitable processing, and then storing it in a computer memory.

[0233] It should be understood that various parts of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc. It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

[0234] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for suppressing harmonics in traction power supply based on robust H∞ control RPC, characterized in that: include: Analyze the power quality of railway traction power supply system; Construct a module engineering model of the vehicle-grid coupled traction power supply system; Build a quadruple RPC model based on robust H∞ control; A locomotive simulation model was constructed and six parallel APF models were designed for power quality analysis.

2. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to claim 1, characterized in that: The analysis of the power quality of the railway traction power supply system includes the parallel quadruple topology. Since the topology of each RPC is consistent and the α power supply arm is symmetrical with the β power supply arm, only the single-side VSC equivalent circuit model is shown; u c is the equivalent voltage of VSC AC side, u T is the AC voltage of the traction network, u s is the AC voltage on the low voltage side, i is the current flowing through the AC side of the VSC, i dc is the current flowing through the DC side of the VSC; VSC AC side equivalent voltage u c It is expressed as: Among them, u c is the equivalent voltage of the VSC AC side, λ represents the PWM modulation depth of the VSC, k c is the voltage u c The amplitude adjustment coefficient, ω is the angular frequency, δ represents the inverter output compared to u s The phase angle of The circuit equations of the AC and DC sides of the VSC are expressed as: Among them, u s is the AC voltage on the low voltage side, and C is the capacitance; The steady-state mathematical model of RPC single-side VSC is expressed as: Among them, i d and i q is the dq component of current i, U s represents the reference phase u s Valid values.

3. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) as claimed in claim 2, characterized in that: The engineering model of the vehicle-grid coupled traction power supply system module includes that the RPC module adopts voltage and current double closed loop control, and the control strategy adopted by the RPC amplitude and phase control is the LMI control method based on robust H∞ control; The state equation of the system is expressed as: Where u is the control input, d is the disturbance, x = [x1 x2] T , x1 and x2 represent state variables; matrix A represents the system matrix, which represents the relationship between the state variables within the system; matrix B represents the input matrix, which represents the impact of the input on the system state; The controller equation is expressed as: U=Kx Among them, the controller gain matrix K = [k1 k2], k1, k2 are controller parameters; The control objective is to achieve x→0 by designing LMI solution; H∞ control aims to minimize the norm of the transfer function from the disturbance input to the system output.

4. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) as claimed in claim 3, characterized in that: The engineering model of the vehicle-grid coupled traction power supply system module includes an H∞ controller including: Design Lyapunov function: V=x T Px Where P is a positive definite matrix; Derivative with respect to V: tidy: Where Q is the intermediate derivation matrix, Q = [P (A + BK)] T + P(A+BK); η=[x T d T ] T , η is a vector consisting of the system state and disturbance; Set output: The output must meet the following performance indicators: Among them, γ is the performance index correlation coefficient, and γ>0; Stability judgment, by constructing the matrix: Analyze the stability of the system and output the convergence result of the system state x: Among them, v max represents the upper bound of the perturbation energy, V(0) is the initial value of the Lyapunov function, P min is the minimum eigenvalue of a positive definite symmetric matrix; The LMI design is expressed as: Let F = KP -1 ,N=P -1 , then P -1 K T =F T , then the first LMI is output: Another LMI is output from the definition of P: N>0,N=N T 。 5. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to claim 4, characterized in that: The quadruple RPC model based on robust H∞ control includes an energy storage device including a lithium battery energy storage part, and a PNGV model is selected; Lithium batteries have two states: charging and discharging. When the battery is in the discharging state, the load current i bat >0, R d 、V a 、V g They are: When the battery is in charging state, the load current i bat <0, R d 、V a 、V g They are: Among them, the variable S b and S g It is expressed as: Among them, V g Indicates the charging voltage tail rise, V a Indicates the maximum saturation voltage drop, R d Represents the battery discharge internal resistance, V a0 Indicates V a Constant value, V a1 Indicates V a Coefficient of variation, SOC represents the state of charge, S a Indicates SOC to V a The impact point, S b For SOC to V g The influence point, R0 represents the internal resistance constant, R1 represents the internal resistance variation coefficient, S d represents the threshold state of charge, i bat Represents the battery current, R c Represents the charging internal resistance, V ga Indicates the charging voltage coefficient.

6. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to claim 5, characterized in that: The said construction of locomotive simulation model and design of six working condition parallel APF models for power quality analysis include parallel APF, which generates current source so that the current source and harmonic current in the power grid are offset; For the selection of the DC side voltage of the APF main circuit, the DC side voltage U dc Affects the ability to compensate for harmonics; Outputting the DC side voltage according to the harmonic frequency and amplitude to be compensated and the capacity of the device; U dc Take the peak value at the connection point between APF and coupling transformer: Wherein, k is the transformation ratio coefficient of the coupling transformer.

7. The method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to claim 6, characterized in that: The construction of the locomotive simulation model and the design of six working conditions parallel APF models for power quality analysis include the selection of the DC side capacitor of the main circuit. Since the DC side capacitor is always in a charging and discharging working state during normal operation of the active filter, it is assumed that the capacitor is always in a charging or discharging state within a cycle, and the maximum allowable deviation of the output DC side capacitor voltage is set to ΔU dcmax , the DC side capacitance of the APF main circuit is: Where C is the DC side capacitance value; PWM is the pulse frequency; is the maximum current passing through the capacitor.

8. A system using the method for suppressing traction power supply harmonics based on robust H∞ control (RPC) as claimed in any one of claims 1 to 7, characterized in that: Including initialization module, RPC model building module, locomotive simulation model building module, locomotive working condition design module; The initialization module is used to analyze the power quality problems of the railway traction power supply system; The RPC model building module is used to build a module engineering model of a vehicle-grid coupled traction power supply system and to construct a quadruple RPC model based on robust H∞ control; The locomotive operating condition design module is used to construct a locomotive simulation model and design six operating conditions.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for suppressing traction power supply harmonics based on robust H∞ control (RPC) according to any one of claims 1 to 7 are implemented.

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