A method for compensating power quality by a railway power conditioner

Abstract

The present application provides a kind of railway power regulator compensation power quality method, belong to the electric power compensation technical field in railway system, method includes the following steps, the compensation capacity mathematical model of railway power regulator under constraint condition is established, in the case where there are infinite solutions in compensation capacity mathematical model, according to boundary constraint, the solution range is reduced, in the solution range, different working conditions are used to solve compensation capacity mathematical model using optimization algorithm, and the best compensation capacity operating point is output. Combined with the operation characteristics of traction power supply system, partial power factor correction is realized through front-end independent regulation strategy, which effectively reduces the dependence on centralized reactive power compensation capacity, improves the steady-state operation performance of the system, and has the advantages of flexible deployment and fast response. It is suitable for the engineering demand of power factor and power quality collaborative control in high-speed railway, urban rail transit and other scenes.

Description

Technical Field

[0001] This invention relates to the field of power compensation technology in railway systems, and in particular to a method for compensating power quality using a railway power regulator. Background Technology

[0002] Electrified railways play a crucial role in economic development due to their powerful carrying capacity and economic benefits. With the development of high-speed rail technology, traditional 27.5 kV single-phase AC electrified railway systems are widely used. However, due to the characteristics of traction loads, this system suffers from significant power quality problems, such as negative sequence current and reactive power. These problems burden the power grid and increase operation and maintenance costs. To address the issues of conventional reactive power, harmonics, and unbalanced operation, Y. Mochinaga et al. proposed a comprehensive power quality solution—the Railway Power Regulator (RPC). Existing Railway Power Regulators (RPCs) generally employ full compensation (FC) and partial compensation (PC) modes. The full compensation mode can provide high power quality, but its large compensation current capacity leads to high initial investment and operating costs. The partial compensation mode, while ensuring power quality, can effectively reduce the compensation current capacity, thus offering greater economic benefits. However, traditional partial compensation strategies require consistent power factor on the grid side, necessitating additional compensation capacity to meet this condition, keeping the compensation capacity requirement high. Therefore, a method for power quality compensation using a railway power regulator is needed. Summary of the Invention

[0003] The purpose of this invention is to provide a method for compensating power quality in railway power regulators, which solves the technical problem that existing railway power regulator compensation methods require the grid-side power factor to be consistent, which necessitates additional compensation capacity to meet this condition, thus keeping the compensation capacity requirement at a relatively high level.

[0004] By employing independent grid-side three-phase power factors, system configuration conditions are simplified, effectively reducing the required compensation capacity and thus lowering the operating cost of railway power regulators. A mathematical model of independent three-phase power factors is established, boundary constraints are used to narrow the solution space, and an optimization algorithm is employed to solve the model, thereby finding the minimum compensation capacity operating point.

[0005] First, the voltage and current parameters of the traction load are obtained. Then, using independently controlled passive or active compensators, the compensation target is calculated based on the power factor setpoint, and pre-compensation is performed without interfering with the operation of the traction load. This invention, combined with the operating characteristics of the traction power supply system, achieves partial power factor correction through an independent front-end adjustment strategy, effectively reducing the dependence on centralized reactive power compensation capacity, improving the system's steady-state operating performance, and offering advantages such as flexible deployment and fast response. It is applicable to engineering needs for coordinated control of power factor and power quality in scenarios such as high-speed railways and urban rail transit.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for compensating power quality using a railway power regulator, the method comprising the following steps:

[0008] Step 1: Establish a mathematical model of the compensation capacity of the railway power regulator under constraints;

[0009] Step 2: When the mathematical model for compensation capacity has infinitely many solutions, narrow the solution range based on boundary constraints;

[0010] Step 3: Within the solution range, use optimization algorithms to solve the mathematical model of compensation capacity for different working conditions;

[0011] Step 4: Run and output the optimal compensation capacity operating point.

[0012] Furthermore, in the mathematical model of compensation capacity in step 1, the three-phase current is expressed as:

[0013]

[0014] Among them, I A I B and I C These represent the currents in phases A, B, and C, respectively. a and I b I represents the α-side current and β-side current on the secondary side. L I cα and I cβ These represent the load current, the α-side RPC compensation current, and the β-side RPC compensation current, respectively, and N1 represents the number of turns of the grid-side and secondary-side coils.

[0015] The secondary side α-side current and β-side current can also be expressed as:

[0016]

[0017] Among them, I ap and Ibp I represents the active components of the α-side current and the β-side current on the secondary side. aq and I bq I represents the reactive components of the α-side current and the β-side current on the secondary side. Lp I cαp and I cβp I represents the active component of the load current, the active component of the α-side RPC compensation current, and the active component of the β-side RPC compensation current, respectively. Lq I cαq and I cβq These represent the reactive components of the load current, the reactive components of the α-side RPC compensation current, and the reactive components of the β-side RPC compensation current, respectively.

[0018] The C-phase power factor can also be written as:

[0019]

[0020] Where angle() represents the angle;

[0021] Formula Substitution I can be obtained Lp and I cαp The relationship is as follows:

[0022]

[0023] Where, θ ac This indicates the angle between the secondary side α-side voltage and the A-phase voltage, which is 30°.

[0024] θ bc θ represents the angle between the secondary side β-side voltage and the B-phase voltage, which is 90°. A θ B and θ C These represent the angles between the A-phase current and the A-phase voltage, the B-phase current and the B-phase voltage, and the C-phase current and the C-phase voltage, respectively.

[0025] The α-side RPC compensation current and the β-side RPC compensation current can also be expressed as:

[0026]

[0027] Where λ is derived from equation λ represents the proportionality coefficient between the active component of the compensation current on the α side and the active component of the load current, which is used to adjust the distribution of active power.

[0028] Three-phase current can be represented by load current and compensation current, that is:

[0029]

[0030] N1 represents the number of turns in the main winding and the secondary winding, while the α-side RPC compensation current and the β-side RPC compensation current can be expressed as:

[0031]

[0032] Where, θ a and θ b Indicates the compensation current I on the α side cα The angle between the voltage on the α side and the compensation current I on the β side cβ The angle between the voltage on the secondary side α and the voltage on the α side, k represents the ratio of the active current transferred by the RPC to the active current of the load, θ L This indicates the angle between the load current and the voltage on the secondary side α.

[0033] The expression for compensation current Substitution The expression for the three-phase current can be obtained, namely:

[0034]

[0035] Among them, I L_Ap I L_Bp and I L_Cp These represent the load current I. L The active power components of phase A, phase B, and phase C; I L_Aq I L_Bq and I L_Cq These represent the load current I. L The reactive components of phase A, phase B, and phase C; I cα_Ap I cα_Bp and I cα_Cp These represent the compensation current I on the α side, respectively. cα The active power components of phase A, phase B, and phase C; I cα_Aq I cα_Bq and I cα_Cq These represent the compensation current I on the α side, respectively. cα The reactive components of phase A, phase B, and phase C; I cβ_Ap I cβ_Bp and I cβ_Cp These represent the compensation current I on the β side, respectively. cβ The active power components of phase A, phase B, and phase C; I cβ_Aq I cβ_Bq and I cβ_Cq These represent the compensation current I on the β side, respectively.cβ The reactive components of phase A, phase B, and phase C.

[0036] Furthermore, the active and reactive components of the three grid-side currents can be expressed as:

[0037]

[0038] According to the formula - The power factor can be expressed by the following formula:

[0039]

[0040] PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively. Ap I Aq I Bp I Bq I Cp and I Cq These represent the active and reactive components of the currents in phases A, B, and C, respectively. It is worth noting that although power factors (PFs) share the same control factor, they do not necessarily need to follow the same PF reference.

[0041] Furthermore, in step 2, the boundary constraint is a power factor boundary constraint, expressed as follows:

[0042]

[0043] Among them, PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively; PF T This indicates the lower bound of the power factor.

[0044] The voltage unbalance boundary constraints are expressed as follows:

[0045]

[0046] Among them, V sn Indicates the secondary side voltage; S d This represents the short-circuit power capacity of the traction substation, taken as 486MW. - Indicates negative sequence current;

[0047] The compensation capacity function is expressed as follows:

[0048]

[0049] Where C represents the compensation capacity, I cα and I cβ These represent the α-side RPC compensation current and the β-side RPC compensation current, respectively.

[0050] Furthermore, the specific process of step 3 is as follows: satisfying the lower bound of PF, I cα and I cβ There are many combinations, but the minimum compensation capacity cannot be determined. Therefore, the fireworks algorithm is used to find the working point with the minimum compensation capacity.

[0051] Each explosion of a group of sparks produces explosive sparks. The formulas for calculating the number of explosive sparks S and the explosion radius R are as follows:

[0052]

[0053]

[0054] Among them, S i R represents the number of sparks produced by the explosion of the i-th Martian individual. i f(x) represents the explosion radius of the i-th Martian individual, c1 and c2 are constants used to limit the number of explosion sparks and the explosion radius, respectively. i Let f(x) represent the fitness value of the i-th Martian individual, and maxf(x) and minf(x) represent the Martian individuals with the worst fitness and the best fitness, respectively. ε is a very small constant that is not zero.

[0055] The following formula is used to limit:

[0056]

[0057]

[0058] Here, `round()` is a rounding function, `c1` is a constant used to limit the number of explosion sparks, `c3` and `c4` are constant variables, and `T`... max R is the maximum number of rounds, t is the current round, and R is the maximum number of rounds. init R represents the initial explosion radius. final This represents the final explosion radius.

[0059] The explosion sparks were generated within the Martian blast radius. The location of the explosion sparks and their Gaussian transform representation are as follows:

[0060]

[0061]

[0062] Where, x i k This represents the position of the i-th individual in the k-th dimension, and rand() generates a random number within a range. opt k This represents the position information of the current best individual in the k-th dimension, and G represents a Gaussian distribution with a mean of 0 and a variance of 1.

[0063] The remapping function for individuals crossing the domain boundary is represented as follows:

[0064]

[0065] Information on superior individuals in the population will be iterated to the next population. Besides retaining the individual with the best fitness, the probability of each candidate spark being selected is as follows:

[0066]

[0067] Where S is the set of candidate individuals, and d(x) is the sum of distances between x and other individuals.

[0068] Further, step 4 involves using the MATLAB platform to solve the mathematical model of compensation capacity under a specific railway operating condition, employing an optimization algorithm to quickly find the minimum compensation capacity operating point within the boundary constraints. Finally, the minimum compensation capacity, the ratio of the active current transferred by the RPC to the load active current, and the α-side compensation current I are output. cα The angle between the voltage on the α side and the secondary side, and the compensation current I on the β side. cβ All parameters of the angle between the voltage on the secondary side and the voltage on the α side.

[0069] The present invention, by adopting the above-described technical solution, has the following beneficial effects:

[0070] This invention acquires the voltage and current parameters of the traction load; then, using independently controlled passive or active compensators, it calculates the compensation target based on the power factor setpoint, performing pre-compensation without interfering with the operation of the traction load. This invention, considering the operating characteristics of the traction power supply system, achieves partial power factor correction through an independent front-end adjustment strategy, effectively reducing reliance on centralized reactive power compensation capacity, improving system steady-state performance, and offering advantages such as flexible deployment and fast response. It is applicable to engineering needs for coordinated control of power factor and power quality in scenarios such as high-speed railways and urban rail transit. Attached Figure Description

[0071] Figure 1 This is a schematic diagram of the modular multilevel converter of the present invention in an electrified railway.

[0072] Figure 2 This is a flowchart of the strategy operation of this invention;

[0073] Figure 3 This invention provides simulation waveform diagrams, including grid current, compensation current, load current, and grid voltage. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are merely to provide the reader with a thorough understanding of one or more aspects of the present invention, and these aspects of the invention can be implemented even without these specific details.

[0075] This invention employs a modular multilevel converter (MMC) as the core compensation device. The system structure is as follows: Figure 1 As shown, reactive power and negative sequence current are compensated by controlling the voltage and current on both sides of α and β.

[0076] The model uses the three-phase power factor as an independent variable, and the formula for calculating its compensation current capacity is as follows:

[0077]

[0078] θ ac θ represents the angle between the secondary side α voltage and the A-phase voltage, which is 30°. bc θ represents the angle between the secondary side β-side voltage and the B-phase voltage, and is 90°; A θ B and θ C θ represents the angle between phase A current and phase A voltage, the angle between phase B current and phase B voltage, and the angle between phase C current and phase C voltage, respectively. L This represents the angle between the load current and the voltage on the secondary side α. Lp Indicates the load current I L The effective weight.

[0079] 3. Setting Constraints

[0080] Voltage imbalance rate condition:

[0081]

[0082] Among them, V sn Indicates the secondary side voltage; Sd This represents the short-circuit power capacity of the traction substation, taken as 486MW; I - This indicates negative sequence current.

[0083] Power factor boundary conditions:

[0084]

[0085] Among them, PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively; PF T This indicates the lower bound of the power factor.

[0086] Algorithm initialization: Set the population size to 100, with each individual representing a compensated solution; Explosion spark generation: Calculate the number and radius of explosion sparks based on fitness; Mutation spark generation: Generate new solutions through Gaussian mutation; Boundary handling: Remap individuals that exceed the boundary; Selection strategy: Retain the best solution and some other high-quality solutions; Iterative update: Repeat the explosion and selection process until the optimal solution is reached.

[0087] Simulation results show that the FD-PC strategy of this invention outperforms the RD-PC strategy in terms of compensation current capacity under different power factor boundaries. Experimental results further verify the effectiveness of this invention, showing that the compensation capacity of the FD-PC strategy is reduced by 14% to 19% compared to the RD-PC strategy.

[0088] The compensation current capacity is optimized by setting a pre-set voltage imbalance rate constraint. The model parameters are optimized using the fireworks algorithm to determine the minimum compensation current capacity. Under different load conditions, the compensation current capacity is reduced by an average of 6.9% to 17.63%.

[0089] The method includes the following steps:

[0090] Step 1: Establish a mathematical model of the compensation capacity of the railway power regulator under constraints.

[0091] In the mathematical model of compensation capacity, the three-phase current is expressed as:

[0092]

[0093] Among them, I A I B and I C These represent the currents in phases A, B, and C, respectively. a and I b I represents the α-side current and β-side current on the secondary side. L I cα and Icβ These represent the load current, the α-side RPC compensation current, and the β-side RPC compensation current, respectively, and N1 represents the number of turns of the grid-side and secondary-side coils.

[0094] The secondary side α-side current and β-side current can also be expressed as:

[0095]

[0096] Among them, I ap and I bp I represents the active components of the α-side current and the β-side current on the secondary side. aq and I bq I represents the reactive components of the α-side current and the β-side current on the secondary side. Lp I cαp and I cβp I represents the active component of the load current, the active component of the α-side RPC compensation current, and the active component of the β-side RPC compensation current, respectively. Lq I cαq and I cβq These represent the reactive components of the load current, the reactive components of the α-side RPC compensation current, and the reactive components of the β-side RPC compensation current, respectively.

[0097] The C-phase power factor can also be written as:

[0098]

[0099] Where angle() represents the angle;

[0100] Formula Substitution I can be obtained Lp and I cαp The relationship is as follows:

[0101]

[0102] Where, θ ac This indicates the angle between the secondary side α-side voltage and the A-phase voltage, which is 30°.

[0103] θ bc θ represents the angle between the secondary side β-side voltage and the B-phase voltage, which is 90°. A θ B and θ C These represent the angles between the A-phase current and the A-phase voltage, the B-phase current and the B-phase voltage, and the C-phase current and the C-phase voltage, respectively.

[0104] The α-side RPC compensation current and the β-side RPC compensation current can also be expressed as:

[0105]

[0106] Where λ is derived from equation λ represents the proportionality coefficient between the active component of the compensation current on the α side and the active component of the load current, which is used to adjust the distribution of active power.

[0107] Three-phase current can be represented by load current and compensation current, that is:

[0108]

[0109] N1 represents the number of turns in the main winding and the secondary winding, while the α-side RPC compensation current and the β-side RPC compensation current can be expressed as:

[0110]

[0111] Where, θ a and θ b Indicates the compensation current I on the α side cα The angle between the voltage on the α side and the compensation current I on the β side cβ The angle between the voltage on the secondary side α and the voltage on the α side, k represents the ratio of the active current transferred by the RPC to the active current of the load, θ L This indicates the angle between the load current and the voltage on the secondary side α.

[0112] The expression for compensation current Substitution The expression for the three-phase current can be obtained, namely:

[0113]

[0114] Among them, I L_Ap I L_Bp and I L_Cp These represent the load current I. L The active power components of phase A, phase B, and phase C; I L_Aq I L_Bq and I L_Cq These represent the load current I. L The reactive components of phase A, phase B, and phase C; I cα_Ap I cα_Bp and I cα_Cp These represent the compensation current I on the α side, respectively. cα The active power components of phase A, phase B, and phase C; I cα_Aq I cα_Bq and Icα_Cq These represent the compensation current I on the α side, respectively. cα The reactive components of phase A, phase B, and phase C; I cβ_Ap I cβ_Bp and I cβ_Cp These represent the compensation current I on the β side, respectively. cβ The active power components of phase A, phase B, and phase C; I cβ_Aq I cβ_Bq and I cβ_Cq These represent the compensation current I on the β side, respectively. cβ The reactive components of phase A, phase B, and phase C.

[0115] The active and reactive components of the three grid-side currents can be expressed as:

[0116]

[0117] According to the formula - The power factor can be expressed by the following formula:

[0118]

[0119] PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively. Ap I Aq I Bp I Bq I Cp and I Cq These represent the active and reactive components of the currents in phases A, B, and C, respectively. It is worth noting that although power factors (PFs) share the same control factor, they do not necessarily need to follow the same PF reference.

[0120] Step 2: When the mathematical model of compensation capacity has infinitely many solutions, narrow the solution range according to the boundary constraints.

[0121] The boundary constraint is a power factor boundary constraint, expressed as follows:

[0122]

[0123] Among them, PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively; PF T This indicates the lower bound of the power factor.

[0124] The voltage unbalance boundary constraints are expressed as follows:

[0125]

[0126] Among them, V sn Indicates the secondary side voltage; S d This represents the short-circuit power capacity of the traction substation, taken as 486MW. - Indicates negative sequence current;

[0127] The compensation capacity function is expressed as follows:

[0128]

[0129] Where C represents the compensation capacity, I cα and I cβ These represent the α-side RPC compensation current and the β-side RPC compensation current, respectively.

[0130] Within the solution scope, optimization algorithms are used to solve the mathematical model of the compensation capacity for different operating conditions. The I value satisfies the lower bound of PF. cα and I cβ There are many combinations, but the minimum compensation capacity cannot be determined. Therefore, the fireworks algorithm is used to find the working point with the minimum compensation capacity.

[0131] Each explosion of a group of sparks produces explosive sparks. The formulas for calculating the number of explosive sparks S and the explosion radius R are as follows:

[0132]

[0133]

[0134] Among them, S i R represents the number of sparks produced by the explosion of the i-th Martian individual. i f(x) represents the explosion radius of the i-th Martian individual, c1 and c2 are constants used to limit the number of explosion sparks and the explosion radius, respectively. i Let f(x) represent the fitness value of the i-th Martian individual, and maxf(x) and minf(x) represent the Martian individuals with the worst fitness and the best fitness, respectively. ε is a very small constant that is not zero.

[0135] The following formula is used to limit:

[0136]

[0137]

[0138] Here, `round()` is a rounding function, `c1` is a constant used to limit the number of explosion sparks, `c3` and `c4` are constant variables, and `T`... max R is the maximum number of rounds, t is the current round, and R is the maximum number of rounds. init R represents the initial explosion radius. final This represents the final explosion radius.

[0139] The explosion sparks were generated within the Martian blast radius. The location of the explosion sparks and their Gaussian transform representation are as follows:

[0140]

[0141]

[0142] Where, x i k This represents the position of the i-th individual in the k-th dimension, and rand() generates a random number within a range. opt k This represents the position information of the current best individual in the k-th dimension, and G represents a Gaussian distribution with a mean of 0 and a variance of 1.

[0143] The remapping function for individuals crossing the domain boundary is represented as follows:

[0144]

[0145] Information on superior individuals in the population will be iterated to the next population. Besides retaining the individual with the best fitness, the probability of each candidate spark being selected is as follows:

[0146]

[0147] Where S is the set of candidate individuals, and d(x) is the sum of distances between x and other individuals.

[0148] Run and output the optimal compensation capacity operating point. On the MATLAB platform, given a specific railway operating condition, use an optimization algorithm to solve the mathematical model of compensation capacity. Within the boundary constraints, quickly find the minimum compensation capacity operating point, and finally output the minimum compensation capacity, the ratio of active current transferred by the RPC to the load active current, and the α-side compensation current I. cα The angle between the voltage on the α side and the secondary side, and the compensation current I on the β side. cβ All parameters of the angle between the voltage on the secondary side and the voltage on the α side.

[0149] The invention acquires the voltage and current parameters of the traction load; then, using independently controlled passive or active compensators, it calculates the compensation target based on the power factor setpoint, performing pre-compensation without interfering with the operation of the traction load. This invention, considering the operating characteristics of the traction power supply system, achieves partial power factor correction through an independent front-end adjustment strategy, effectively reducing reliance on centralized reactive power compensation capacity, improving system steady-state performance, and offering advantages such as flexible deployment and fast response. It is applicable to engineering needs for coordinated control of power factor and power quality in scenarios such as high-speed railways and urban rail transit.

[0150] Matters not covered in this invention are common knowledge.

[0151] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for compensating power quality using a railway power regulator, characterized in that: The method includes the following steps: Step 1: Establish a mathematical model of the compensation capacity of the railway power regulator under constraints; Step 2: When the mathematical model for compensation capacity has infinitely many solutions, narrow the solution range based on boundary constraints; Step 3: Within the solution range, use optimization algorithms to solve the mathematical model of compensation capacity for different working conditions; Step 4: Run and output the optimal compensation capacity operating point.

2. The method for compensating power quality using a railway power regulator according to claim 1, characterized in that, In the mathematical model of compensation capacity in step 1, the three-phase current is expressed as: Among them, I A I B and I C These represent the currents in phases A, B, and C, respectively. a and I b I represents the α-side current and β-side current on the secondary side. L I cα and I cβ These represent the load current, the α-side RPC compensation current, and the β-side RPC compensation current, respectively, and N1 represents the number of turns of the grid-side and secondary-side coils. The secondary side α-side current and β-side current can also be expressed as: Among them, I ap and I bp I represents the active components of the α-side current and the β-side current on the secondary side. aq and I bq I represents the reactive components of the α-side current and the β-side current on the secondary side. Lp I cαp and I cβp I represents the active component of the load current, the active component of the α-side RPC compensation current, and the active component of the β-side RPC compensation current, respectively. Lq I cαq and I cβq These represent the reactive components of the load current, the reactive components of the α-side RPC compensation current, and the reactive components of the β-side RPC compensation current, respectively. The C-phase power factor can also be written as: Where angle() represents the angle; Formula Substitution I can be obtained Lp and I cαp The relationship is as follows: Where, θ ac This indicates the angle between the secondary side α-side voltage and the A-phase voltage, which is 30°. θ bc θ represents the angle between the secondary side β-side voltage and the B-phase voltage, which is 90°. A θ B and θ C These represent the angles between the A-phase current and the A-phase voltage, the B-phase current and the B-phase voltage, and the C-phase current and the C-phase voltage, respectively. The α-side RPC compensation current and the β-side RPC compensation current can also be expressed as: Where λ is derived from equation λ represents the proportionality coefficient between the active component of the compensation current on the α side and the active component of the load current, which is used to adjust the distribution of active power. Three-phase current can be represented by load current and compensation current, that is: N1 represents the number of turns in the main winding and the secondary winding, while the α-side RPC compensation current and the β-side RPC compensation current can be expressed as: Where, θ a and θ b Indicates the compensation current I on the α side cα The angle between the voltage on the α side and the compensation current I on the β side cβ The angle between the voltage on the secondary side α and the voltage on the α side, k represents the ratio of the active current transferred by the RPC to the active current of the load, θ L This indicates the angle between the load current and the voltage on the secondary side α. The expression for compensation current Substitution The expression for the three-phase current can be obtained, namely: Among them, I L_Ap I L_Bp and I L_Cp These represent the load current I. L The active power components of phase A, phase B, and phase C; I L_Aq I L_Bq and I L_Cq These represent the load current I. L The reactive components of phase A, phase B, and phase C; I cα_Ap I cα_Bp and I cα_Cp These represent the compensation current I on the α side, respectively. cα The active power components of phase A, phase B, and phase C; I cα_Aq I cα_Bq and I cα_Cq These represent the compensation current I on the α side, respectively. cα The reactive components of phase A, phase B, and phase C; I cβ_Ap I cβ_Bp and I cβ_Cp These represent the compensation current I on the β side, respectively. cβ The active power components of phase A, phase B, and phase C; I cβ_Aq I cβ_Bq and I cβ_Cq These represent the compensation current I on the β side, respectively. cβ The reactive components of phase A, phase B, and phase C.

3. The method for compensating power quality using a railway power regulator according to claim 2, characterized in that: The active and reactive components of the three grid-side currents can be expressed as: According to the formula - The power factor can be expressed by the following formula: PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively. Ap I Aq I Bp I Bq I Cp and I Cq These represent the active and reactive components of the currents in phases A, B, and C, respectively. It is worth noting that although power factors (PFs) share the same control factor, they do not necessarily need to follow the same PF reference.

4. The method for compensating power quality using a railway power regulator according to claim 1, characterized in that, In step 2, the boundary constraint is the power factor boundary constraint, as shown below: Among them, PF A PF B and PF C These represent the power factor of phase A, the power factor of phase B, and the common power factor of phase C, respectively; PF T This indicates the lower bound of the power factor. The voltage unbalance boundary constraints are expressed as follows: Among them, V sn Indicates the secondary side voltage; S d This represents the short-circuit power capacity of the traction substation, taken as 486MW. - Indicates negative sequence current; The compensation capacity function is expressed as follows: Where C represents the compensation capacity, I cα and I cβ These represent the α-side RPC compensation current and the β-side RPC compensation current, respectively.

5. A method for compensating power quality using a railway power regulator according to claim 1, characterized in that, The specific process of step 3 is to satisfy the lower bound of PF. cα and I cβ There are many combinations, but the minimum compensation capacity cannot be determined. Therefore, the fireworks algorithm is used to find the working point with the minimum compensation capacity. Each explosion of a group of sparks produces explosive sparks. The formulas for calculating the number of explosive sparks S and the explosion radius R are as follows: Among them, S i R represents the number of sparks produced by the explosion of the i-th Martian individual. i f(x) represents the explosion radius of the i-th Martian individual, c1 and c2 are constants used to limit the number of explosion sparks and the explosion radius, respectively. i Let f(x) represent the fitness value of the i-th Martian individual, and maxf(x) and minf(x) represent the Martian individuals with the worst fitness and the best fitness, respectively. ε is a very small constant that is not zero. The following formula is used to limit: Here, `round()` is a rounding function, `c1` is a constant used to limit the number of explosion sparks, `c3` and `c4` are constant variables, and `T`... max R is the maximum number of rounds, t is the current round, and R is the maximum number of rounds. init R represents the initial explosion radius. final This represents the final explosion radius. The explosion sparks were generated within the Martian blast radius. The location of the explosion sparks and their Gaussian transform representation are as follows: Where, x i k This represents the position of the i-th individual in the k-th dimension, and rand() generates a random number within a range. opt k This represents the position information of the current best individual in the k-th dimension, and G represents a Gaussian distribution with a mean of 0 and a variance of 1. The remapping function for individuals crossing the domain boundary is represented as follows: Information on superior individuals in the population will be iterated to the next population. Besides retaining the individual with the best fitness, the probability of each candidate spark being selected is as follows: Where S is the set of candidate individuals, and d(x) is the sum of distances between x and other individuals.

6. A method for compensating power quality using a railway power regulator according to claim 1, characterized in that, Step 4 involves using the MATLAB platform to solve the mathematical model of compensation capacity under a specific railway operating condition, employing an optimization algorithm to quickly find the minimum compensation capacity operating point within the boundary constraints. Finally, the minimum compensation capacity, the ratio of the active current transferred by the RPC to the load active current, and the α-side compensation current I are output. cα The angle between the voltage on the α side and the secondary side, and the compensation current I on the β side. cβ All parameters of the angle between the voltage on the secondary side and the voltage on the α side.

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