Method and device for generating a pv curve of a regenerative braking based traction power supply system

Abstract

The application provides a traction power supply system PV curve generation method and device based on regenerative braking, relates to the data processing technical field of a traction power supply system, and determines a feasible solution expression based on a locomotive active power expression and an infeasible solution expression based on a locomotive reactive power expression by respectively constructing the locomotive active power expression and the locomotive reactive power expression. The PV curve generation condition is that the locomotive active power is less than 0, the PV curve corresponding to the feasible solution under the regenerative braking condition can be generated based on the feasible solution expression, the PV curve corresponding to the infeasible solution under the regenerative braking condition can be generated based on the infeasible solution expression, and the feasible solution expression and the infeasible solution expression are equations about the locomotive active power. When the PV curve is generated, the PV curve including the regenerative braking condition can be quickly generated.

Description

Technical Field

[0001] This application relates to the field of traction power supply system data processing technology, specifically to a method and apparatus for generating PV curves in a traction power supply system based on regenerative braking. Background Technology

[0002] With the continuous development of the economy in mountainous areas, numerous mountain railways are being planned in western China. High-altitude mountain railways typically have significant elevation differences, sometimes exceeding 3000 meters, inevitably leading to long, steep slopes. Locomotives need to operate at full power uphill, while regenerative braking is generally used downhill. Regenerative braking refers to the process where, during deceleration or descent, the traction motor converts into a generator, producing braking torque and feeding excess electrical energy back to the traction network. On long slopes, due to the continuous effect of gravity, the locomotive remains in a regenerative braking state for extended periods, continuously feeding power back to the traction network, resulting in a negative active power. However, this braking energy causes a voltage rise in the traction network, potentially leading to discharge through the train roof gap and brake failure. When this voltage exceeds the 29kV specified by railway standards, it may cause the onboard circuit breaker to trip, affecting normal railway operation. This phenomenon presents a contradiction in the design of traction power supply systems on long, steep slopes: when locomotives operate at full power uphill, the traction grid voltage decreases, and the traction grid bus voltage should be kept as high as possible; conversely, when locomotives brake downhill, the returned power may raise the traction grid voltage, and the traction grid bus voltage should be kept as low as possible. Existing research has not fully investigated the locomotive voltage rise characteristics, and studies on the PV curves of the traction power supply system are limited to traction conditions, without in-depth research on the PV curves under regenerative braking conditions. Therefore, studying the voltage rise mechanism of the traction grid-locomotive system on long, steep slopes has significant practical application value for the planning and design of the traction power supply system's bus voltage, transformers, and traction grid parameters. Summary of the Invention

[0003] This application provides a method and apparatus for generating PV curves of a traction power supply system based on regenerative braking, which can generate PV curves including regenerative braking conditions in a relatively simple way.

[0004] This application provides a method for generating PV curves in a traction power supply system based on regenerative braking, comprising:

[0005] Construct expressions for the locomotive's active power and reactive power;

[0006] The feasible and infeasible solution expressions are determined based on the locomotive active power expression and the locomotive reactive power expression;

[0007] Based on feasible and infeasible solution expressions, PV curves including regenerative braking conditions are generated with the locomotive active power being less than 0 as the generation condition, and PV curves including traction conditions are generated with the locomotive active power being greater than 0 as the generation condition.

[0008] Optionally, the expression for the locomotive's active power includes:

[0009] ;

[0010] The expression for locomotive reactive power can include:

[0011] ;

[0012] The first intermediate variable expression can include:

[0013] ;

[0014] The second intermediate expression can include:

[0015] ;

[0016] The third intermediate expression can include:

[0017] ;

[0018] in, Indicates active power. Indicates reactive power. This indicates the V / V traction transformer turns ratio. Indicates the first intermediate variable. Indicates the locomotive voltage amplitude. Indicates the second intermediate variable. Indicates the phase voltage amplitude of the power grid source. Indicates the phase angle of the locomotive voltage. Indicates the third intermediate variable. This indicates the resistance of the traction transformer. This represents the resistance per unit length of the T-line. This represents the resistance per unit length of the R-line. This represents the mutual resistance per unit length between the T-line and the R-line. Indicates the distance to the target. Indicates the reactance of the traction transformer. This represents the reactance per unit length of the T-line. This represents the reactance per unit length of the R-line. This represents the mutual reactance per unit length between the T-line and the R-line. This represents the equivalent reactance.

[0019] Optionally, the feasible solution expression includes:

[0020] ;

[0021] ;

[0022] in, This indicates a feasible solution. This indicates the first solution.

[0023] Optionally, based on the feasible and infeasible solution expressions, and with the locomotive's active power being less than 0 as the PV curve generation condition, a PV curve including regenerative braking conditions is generated, including:

[0024] Determine the equivalent resistance calculated based on the power factor and determine the target conditions based on the equivalent resistance calculated based on the power factor; the target conditions characterize whether there are extreme points in the PV curve of the feasible solution under regenerative braking conditions;

[0025] Based on the objective conditions and feasible solution expressions, the PV curve is generated with the locomotive active power being less than 0 as the PV curve generation condition, including feasible solutions under regenerative braking conditions.

[0026] Based on the expression of infeasible solutions, and taking the locomotive's active power being less than 0 as the condition for generating PV curves, PV curves including infeasible solutions under regenerative braking conditions are generated.

[0027] Optionally, the formula for calculating the equivalent resistance based on the power factor is as follows:

[0028] ;

[0029] ;

[0030] in, This represents the equivalent resistance calculated based on the power factor. Indicates low-voltage open-circuit voltage. Indicates the system short-circuit capacity. Indicates the first substitute quantity. This indicates the second substitute quantity.

[0031] Optionally, the target conditions include:

[0032] When the equivalent resistance calculated by the power factor is less than or equal to 0, the PV curve of the locomotive active power is less than 0 and monotonically increasing in the first interval; the left endpoint of the first interval is the left limit point of the active power of the PV curve, the right endpoint of the first interval is 0, and the first interval is a left-closed and right-open interval.

[0033] When the equivalent resistance calculated by the power factor is greater than 0, the PV curve of the locomotive active power is less than 0. It is monotonically increasing in the first sub-interval and monotonically decreasing in the second sub-interval. The first interval includes the first sub-interval and the second sub-interval. The first sub-interval and the second sub-interval are obtained according to the extreme point determination formula.

[0034] Optionally, the formula for determining the extreme point includes:

[0035] ;

[0036] ;

[0037] ;

[0038] in, Indicates the extreme point of active power. Indicates the voltage extreme point, This represents the equivalent resistance calculated based on the power factor. Indicates low-voltage open-circuit voltage. This indicates the intermediate conversion amount.

[0039] Optionally, the formula for determining the left limit point of active power includes:

[0040] ;

[0041] in, This indicates the left limit point of active power.

[0042] Optionally, infeasible solution expressions include:

[0043] ;

[0044] ;

[0045] in, Indicates an infeasible solution. This indicates the second solution.

[0046] To achieve the above and other related objectives, this application provides a PV curve generation device for a traction power supply system based on regenerative braking, comprising:

[0047] The first data processing module is used to construct the locomotive active power expression and the locomotive reactive power expression;

[0048] The second data processing module is used to determine the feasible solution expression and the infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression.

[0049] The third data processing module is used to generate PV curves including regenerative braking conditions based on feasible and infeasible solution expressions, with the locomotive active power being less than 0 as the generation condition, and to generate PV curves including traction conditions with the locomotive active power being greater than 0 as the condition.

[0050] As described above, the PV curve generation method and apparatus for a traction power supply system based on regenerative braking provided in this application have the following beneficial effects:

[0051] This application discloses a method for generating PV curves in a traction power supply system based on regenerative braking. This method constructs expressions for the locomotive's active power and reactive power, respectively. Based on the locomotive's active power expression, a feasible solution expression is determined, and based on the locomotive's reactive power expression, an infeasible solution expression is determined. Using a locomotive active power less than 0 as the PV curve generation condition, the method generates PV curves corresponding to feasible solutions under regenerative braking conditions based on feasible solution expressions, and PV curves corresponding to infeasible solutions under regenerative braking conditions based on infeasible solution expressions. The feasible and infeasible solution expressions are equations concerning the locomotive's active power, facilitating the rapid generation of PV curves including those for regenerative braking conditions.

[0052] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0054] Figure 1 This is a flowchart illustrating an exemplary embodiment of the present application of a method for generating PV curves in a traction power supply system based on regenerative braking;

[0055] Figure 2 This is a schematic diagram of a traction power supply system with a direct power supply method and return line;

[0056] Figure 3 This is a schematic diagram of the cross-sectional structure of the direct supply traction network;

[0057] Figure 4 This is a schematic diagram of the equivalent circuit of the upper-level three-phase power grid - traction power supply - locomotive;

[0058] Figure 5 It is the locomotive voltage PV curve that takes into account regenerative braking power;

[0059] Figure 6 It is a hardware-in-the-loop semi-physical simulation platform;

[0060] Figure 7 This is a schematic diagram of the hardware-in-the-loop experimental system structure;

[0061] Figure 8 This is a comparison chart of the hardware-in-the-loop simulation results and the theoretical curves of the PV curve of the traction power supply system;

[0062] Figure 9 It is a hardware-in-the-loop limit simulation curve of the PV curve of the traction power supply system;

[0063] Figure 10 This is a structural block diagram of a PV curve generation device for a traction power supply system based on regenerative braking, as illustrated in an exemplary embodiment of this application. Detailed Implementation

[0064] The embodiments of this application will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be understood that the preferred embodiments are only for illustrating this application and are not intended to limit the scope of protection of this application.

[0065] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. Therefore, the drawings only show the components related to this application and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0066] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the present application. However, it will be apparent to those skilled in the art that embodiments of the present application may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the present application.

[0067] Please see Figure 1 , Figure 1 This is a flowchart illustrating a method for generating PV curves in a traction power supply system based on regenerative braking, as shown in an exemplary embodiment of this application. (Reference) Figure 1 It can be seen that the method for generating the PV curve of the traction power supply system based on regenerative braking can include:

[0068] Step S110: Construct the expressions for the locomotive's active power and reactive power.

[0069] In one embodiment of this application, expressions for the active power and reactive power of the locomotive can be constructed.

[0070] A traction substation, also known as a traction power station, is a facility that converts high-voltage electricity from the local power grid into single-phase alternating current suitable for electric locomotives. The busbar is a conductor within the traction substation that collects and distributes electrical energy. The distance between the locomotive and the traction substation busbar represents the electrical distance along the railway line from the locomotive to the traction substation to which it supplies power. The locomotive voltage amplitude is a function of both the locomotive's power and the power supply distance. With the target distance (the distance between the locomotive and the traction substation busbar) fixed, the locomotive voltage amplitude can be obtained based on the locomotive's active and reactive power.

[0071] For example, when simulating and solving the PV curve under regenerative braking conditions before the locomotive is actually in operation, the user can set the target distance.

[0072] For example, the expression for the active power of a locomotive may include:

[0073] ;

[0074] The expression for locomotive reactive power can include:

[0075] ;

[0076] The first intermediate variable expression can include:

[0077] ;

[0078] The second intermediate expression can include:

[0079] ;

[0080] The third intermediate expression can include:

[0081] ;

[0082] in, Indicates active power. Indicates reactive power. This indicates the V / V traction transformer turns ratio. Indicates the first intermediate variable. Indicates the locomotive voltage amplitude. Indicates the second intermediate variable. Indicates the phase voltage amplitude of the power grid source. Indicates the phase angle of the locomotive voltage. Indicates the third intermediate variable. This indicates the resistance of the traction transformer. This represents the resistance per unit length of the T-line. This represents the resistance per unit length of the R-line. This represents the mutual resistance per unit length between the T-line and the R-line. Indicates the distance to the target. Indicates the reactance of the traction transformer. This represents the reactance per unit length of the T-line. This represents the reactance per unit length of the R-line. This represents the mutual reactance per unit length between the T-line and the R-line. This represents the equivalent reactance.

[0083] For example, please refer to Figures 2 to 4 According to Thevenin's theorem, the upstream power grid can be equivalently replaced by an ideal three-phase power source and reactances in series. This represents the equivalent reactance. This indicates the V / V traction transformer turns ratio. This represents the equivalent impedance of the low-voltage side of the traction transformer. This indicates the distance between the locomotive and the traction depot busbar. This represents the impedance per unit length of line T. R represents the impedance per unit length of the line. This represents the mutual impedance between the T-line and R-line per unit length. The traction network impedance can be calculated using Carson's theory.

[0084] Based on the voltage relationship between the high and low voltage sides of the traction transformer, the first expression can be obtained:

[0085] ;

[0086] in, express Figure 4 The voltage at midpoint 3, express Figure 4 The voltage at midpoint 4, express Figure 4 Voltage at midpoint 5.

[0087] Based on the relationship between the high and low voltage sides of the traction transformer, the second expression can be obtained:

[0088] ;

[0089] in, express Figure 4 The current at midpoint 1, express Figure 4 The current at midpoint 7, express Figure 4 The current at midpoint 2.

[0090] Applying Ohm's law to the high-voltage side of the traction transformer, we can obtain the third and fourth expressions. The third expression can be expressed as:

[0091] ;

[0092] The fourth expression can be represented as:

[0093] ;

[0094] in, express Figure 4 The voltage at midpoint 1, Represents the imaginary part of a complex number. express Figure 4 Voltage at midpoint 2.

[0095] Substituting the third and fourth expressions into the first expression, we get the fifth expression:

[0096] .

[0097] Applying Ohm's law to the low-voltage side of the traction transformer, we can obtain the sixth and seventh expressions. The sixth expression can be expressed as:

[0098] ;

[0099] The seventh expression can be represented as:

[0100] ;

[0101] in, express Figure 4 The voltage difference between the voltage at midpoint 7 and the voltage at point 8 This indicates the resistance of the traction transformer. Indicates the reactance of the traction transformer. This indicates the impedance of the traction transformer. This represents the resistance per unit length of the T-line. This represents the reactance per unit length of the T-line. This represents the impedance per unit length of the T-line. This represents the resistance per unit length of the R-line. This represents the reactance per unit length of the R-line. This represents the impedance per unit length of the R-line. This represents the mutual resistance per unit length between the T-line and the R-line. This represents the mutual reactance per unit length between the T-line and the R-line. This represents the mutual impedance per unit length between the T-line and the R-line.

[0102] Substituting the sixth and seventh expressions into the fifth expression, we obtain the eighth expression:

[0103] .

[0104] Assuming the upstream power grid is symmetrical, then the ninth expression can be obtained:

[0105] .

[0106] Substituting the ninth expression into the eighth expression and taking its conjugate, we obtain the tenth expression:

[0107] ;

[0108] in, express Figure 4 The conjugate complex number of the current at midpoint 7.

[0109] The locomotive resumption rate can then be expressed as:

[0110] ;

[0111] in, Indicates active power. This indicates reactive power.

[0112] Based on the expression for the complex power of the locomotive, we can obtain the expressions for the locomotive's active power and reactive power.

[0113] Step S120: Determine the feasible solution expression and the infeasible solution expression based on the locomotive's active power expression and reactive power expression.

[0114] In one embodiment of this application, feasible and infeasible solution expressions can be obtained by performing algebraic operations on the locomotive's active power expression and reactive power expression.

[0115] Optionally, the active power expression and reactive power expression of the locomotive can be rearranged, squared, and then added together to obtain the first solution expression, which can be expressed as:

[0116] ;

[0117] By substituting the square of the locomotive voltage amplitude, we obtain the second solution expression, which can be expressed as:

[0118] ;

[0119] in, , This refers to the amount of replacement.

[0120] Based on the second solution expression, feasible and infeasible solution expressions are obtained.

[0121] Feasible solution expressions can include:

[0122] ;

[0123] ;

[0124] Infeasible solution expressions can include:

[0125] ;

[0126] ;

[0127] in, This indicates a feasible solution. Indicates an infeasible solution. This represents the first solution. This indicates the second solution.

[0128] It should be noted that a feasible solution, also known as a high-pressure solution, is the equilibrium point where the system can operate stably. An infeasible solution, also known as a low-pressure solution, is the unstable equilibrium point of the system.

[0129] Step S130: Based on the feasible and infeasible solution expressions, a PV curve including regenerative braking is generated with the locomotive active power less than 0 as the PV curve generation condition, and a PV curve including traction is generated with the locomotive active power greater than 0 as the condition.

[0130] Among them, a locomotive active power of less than 0 indicates regenerative braking condition, and a locomotive active power of greater than 0 indicates traction condition.

[0131] In one embodiment of this application, after obtaining the feasible and infeasible solution expressions, a PV curve including regenerative braking conditions can be generated based on the feasible and infeasible solution expressions, with the locomotive active power being less than 0 as the PV curve generation condition. Alternatively, a PV curve including traction conditions can be generated based on the feasible and infeasible solution expressions, with the locomotive active power being greater than 0 as the PV curve generation condition. That is, a PV curve including regenerative braking conditions can be generated independently based on the feasible and infeasible solution expressions, with the locomotive active power being less than 0 as the condition; a PV curve including traction conditions can be generated independently based on the feasible and infeasible solution expressions, with the locomotive active power being greater than 0 as the condition; and a PV curve including both regenerative braking and traction conditions can be generated based on the feasible and infeasible solution expressions, with both the locomotive active power being less than 0 and the active power being greater than 0 as conditions.

[0132] Based on the above feasible and infeasible solution expressions, it can be found that the locomotive voltage amplitude is a function of two variables: the locomotive's active power and the target distance, that is:

[0133] ;

[0134] If the target distance is fixed, the relationship between the locomotive's active power and the locomotive's voltage amplitude can be obtained, which is the PV curve.

[0135] It should be noted that in the process of obtaining the PV curve based on the feasible and infeasible solution expressions, under the premise of a fixed target distance, the locomotive active power value can be directly set and substituted into the feasible or infeasible solution expression to obtain the locomotive voltage amplitude. This simplifies the PV curve solution process, achieves a fast solution effect, and improves the efficiency of PV curve generation.

[0136] Optionally, step S140, which generates a PV curve including regenerative braking conditions based on feasible and infeasible solution expressions and with the locomotive's active power being less than 0 as the PV curve generation condition, may include steps S131 to S133.

[0137] Step S131: Determine the equivalent resistance calculated by the power factor and determine the target conditions based on the equivalent resistance calculated by the power factor.

[0138] Among them, the objective condition characterizes whether there are extreme points in the PV curve of the feasible solution under the regenerative braking condition.

[0139] Target conditions may include:

[0140] When the equivalent resistance calculated by the power factor is less than or equal to 0, the PV curve of the locomotive active power is less than 0 and monotonically increasing in the first interval; the left endpoint of the first interval is the left limit point of the active power of the PV curve, the right endpoint of the first interval is 0, and the first interval is a left-closed and right-open interval.

[0141] When the equivalent resistance calculated by the power factor is greater than 0, the PV curve of the locomotive active power is less than 0. It is monotonically increasing in the first sub-interval and monotonically decreasing in the second sub-interval. The first interval includes the first sub-interval and the second sub-interval. The first sub-interval and the second sub-interval are obtained according to the extreme point determination formula.

[0142] In the process of solving the PV curve, the operator needs to pre-set simulation parameters such as the locomotive's active power and power factor. The locomotive's reactive power can be determined based on the power factor and the locomotive's active power.

[0143] For example, when the power factor lags, the locomotive reactive power expression is as follows:

[0144] ;

[0145] in, This represents the locomotive power factor.

[0146] For example, when the power factor is leading, the locomotive reactive power expression is as follows:

[0147] ;

[0148] The system short-circuit capacity can be set as follows: The following relationship exists between the system short-circuit capacity and the equivalent reactance:

[0149] ;

[0150] The formula for determining the equivalent reactance can then be expressed as:

[0151] ;

[0152] in, Indicates the system short-circuit capacity. Represents equivalent reactance. This indicates the amplitude of the phase voltage of the power grid source.

[0153] For example, the expression for low-voltage no-load voltage can be expressed as:

[0154] ;

[0155] in, This indicates the low-voltage open-circuit voltage.

[0156] For example, when the power factor lags, the formulas for determining the locomotive reactive power, equivalent reactance, low-voltage side no-load voltage, the second intermediate quantity expression, and the third intermediate quantity expression are substituted into the expression of the first solution in the feasible solution expression to obtain the first solution replacement formula. The first solution replacement formula can be expressed as:

[0157] ;

[0158] in, This represents the equivalent resistance calculated based on the power factor. This indicates the intermediate conversion amount.

[0159] The equivalent resistance calculated using the power factor can be expressed as:

[0160] ;

[0161] Intermediate conversion quantities can be expressed as:

[0162] ;

[0163] The first and second substitution quantities can be expressed as:

[0164] ;

[0165] in, Indicates the first substitute quantity. This indicates the second substitute quantity.

[0166] For example, when the power factor is leading, the formulas for determining the locomotive reactive power, equivalent reactance, low-voltage side no-load voltage, the second intermediate quantity expression, and the third intermediate quantity expression are substituted into the expression of the first solution in the feasible solution expression to obtain the first solution replacement formula. The first solution replacement formula can be expressed as:

[0167] ;

[0168] in, This represents the equivalent resistance calculated based on the power factor. This indicates the intermediate conversion amount.

[0169] The equivalent resistance calculated using the power factor can be expressed as:

[0170] ;

[0171] Intermediate conversion quantities can be expressed as:

[0172] ;

[0173] The first and second substitution quantities can be expressed as:

[0174] ;

[0175] in, Indicates the first substitute quantity. This indicates the second substitute quantity.

[0176] For example, analyzing the first solution expression, since This represents the square of the locomotive voltage amplitude, therefore Since it is a non-negative real number, we need to examine the intermediate equation in the first solution substitution formula:

[0177] ;

[0178] The intermediate equation is a... The discriminant of the quadratic equation in one variable is:

[0179] ;

[0180] The two roots of the intermediate equation are:

[0181] ;

[0182] To ensure If there are real solutions, then we need to guarantee .

[0183] and These are the left and right limit points of the PV curve. In traditional power systems, only the positive power limit point P2 on the right is considered, while the negative power limit point P1 on the left is rarely given attention.

[0184] When the locomotive is in regenerative braking mode, i.e., P < 0, by differentiating the active power P using the first solution substitution formula and setting the derivative equal to 0, we can obtain the active power derivative formula:

[0185] ;

[0186] The above formula can then be further simplified to:

[0187] ;

[0188] because Analysis shows that whether the simplified active power derivative formula has a solution depends on the equivalent resistance calculated from the power factor. The sign of the power factor. Therefore, it is necessary to discuss two cases based on whether the power factor is leading or lagging.

[0189] When the locomotive power factor lags, P < 0 under regenerative braking conditions. The expression for the equivalent resistance calculated from the power factor is as follows:

[0190] ;

[0191] 1) If Then the simplified formula for the active power derivative has no solution, and the active power derivative formula... This indicates the first solution. It is monotonically increasing on the interval [P1, 0);

[0192] 2) If Then the simplified formula for the derivative of active power has a unique negative solution:

[0193] ;

[0194] And there are

[0195] ;

[0196] The above analysis shows that when There must exist a negative real number of active power on the PV curve. This allows the locomotive voltage to rise to its maximum value. Substituting the unique negative solution of the simplified active power derivative formula into the feasible solution expression, we can obtain this maximum value as:

[0197] ;

[0198] In addition, when Sometimes, ,show In the interval The upper part is monotonically increasing, that is... It is monotonically increasing in the first interval. When Sometimes, ,show In the interval The upper part is monotonically decreasing, that is... It is monotonically decreasing in the second interval.

[0199] Step S132: Based on the objective conditions and feasible solution expressions, and taking the locomotive active power less than 0 as the PV curve generation condition, generate PV curves including feasible solutions under regenerative braking conditions.

[0200] In one embodiment of this application, a PV curve including a feasible solution under regenerative braking conditions can be generated based on the target conditions and feasible solution expressions, with the locomotive active power being less than 0 as the PV curve generation condition.

[0201] Based on the analysis in step S131, the PV curve of the locomotive voltage can be plotted. The sign of the PV curve can be divided into two groups:

[0202] (1) When At that time, the PV curve is as follows Figure 5 (a) and Figure 5 As shown in (b). From 5(a), it can be seen that the entire PV curve can be composed of two curves, upper and lower. The red curve corresponds to a feasible solution, and the blue curve corresponds to an infeasible solution. From 5(b), it can also be seen that the entire PV curve can be considered as composed of two curves, left and right. The orange curve on the left represents the PV curve under regenerative braking, and the green curve on the right represents the PV curve under traction. It can be seen that in this case, the PV curve under regenerative braking and the PV curve under traction have similar patterns; both gradually decrease the voltage as the power increases, and there is a limiting power (P1 under regenerative braking and P2 under traction).

[0203] (2) When The PV curves are shown in Figures 5(c) and (d). It can be observed that the PV curve under regenerative braking conditions exhibits a different variation pattern compared to the PV curve under traction conditions. Under regenerative braking conditions, as the braking power increases, the locomotive voltage first increases and then decreases, exhibiting a limiting voltage. This indicates that a higher braking power does not necessarily lead to a greater rise in locomotive voltage. When the locomotive braking power is greater than... At that time, the locomotive voltage will actually decrease, and there will be a limit to the braking power. Because excessively high locomotive voltage can lead to traction shutdown or reduced power operation, standards stipulate that locomotive voltage must not exceed 29kV. This necessitates that traction power supply systems distributed on long, steep slopes must consider the control of the low-voltage bus voltage of the traction transformer. Setting the bus voltage too high can easily cause the locomotive voltage to exceed the upper limit, while setting it too low can easily cause the traction network voltage to exceed the lower limit. Therefore, the proposed locomotive PV curve formula can provide theoretical support for the design of the traction network bus voltage on long, steep slopes.

[0204] It should be noted that the power factor of the locomotive is generally between -0.95 and -1 under regenerative braking conditions. Therefore, in most cases, only the situation in 5(c) will occur.

[0205] When the locomotive power factor is leading, the following formula applies:

[0206] ;

[0207] at this time, The situation is similar to that of locomotive power factor lag (2). That is, there must be a negative real active power PMP on the PV curve that can make the locomotive voltage rise to the maximum value. The PV curves are shown in 5 (c) and (d), and there will be no monotonically decreasing situation as in 5 (a) and (b).

[0208] Step S133: Based on the infeasible solution expression, and taking the locomotive active power less than 0 as the PV curve generation condition, generate PV curves including infeasible solutions under regenerative braking conditions.

[0209] In one embodiment of this application, a PV curve including infeasible solutions under regenerative braking conditions can be generated based on the expression of infeasible solutions, with the locomotive active power being less than 0 as the PV curve generation condition.

[0210] After obtaining the PV curve, the peak (maximum power point) of the PV curve is determined. When the train load demand exceeds the power at this point, the system will lose stability, and the voltage will drop sharply. Analyzing the distance between the current operating point and the peak can assess the voltage stability margin of the system.

[0211] For example, to verify the accuracy of the locomotive voltage PV curve, a system was built as follows: Figure 6 The hardware-in-the-loop (HIL) simulation platform shown is a real-time circuit simulator based on an FPGA (NI PXIe-FPGA-7868R), capable of simulating various power supplies, different power grid types, and different IGBT topologies. The real-time digital controller (NI PXIe-8821-7846R) is a practical industrial controller based on a rapid control prototype, responsible for running the control algorithm, acquiring circuit voltage and current, and outputting digital control signals. I / O boards facilitate the analog / digital signal connection between the real-time circuit simulator and the controller. An oscilloscope displays various voltage and current waveforms during system operation. The host computer, equipped with StarSim software, can display, record, and save all data during system operation.

[0212] Hardware-in-the-loop experimental system architecture as follows Figure 7 As shown, the system consists of a three-phase power supply, a V / V traction transformer, sub-traction network 1, sub-traction network 2, and an AC-DC-AC locomotive. The lengths of sub-traction network 1 and sub-traction network 2 can be arbitrarily changed to simulate the relative motion between the locomotive and the traction network. The rectifier uses transient direct current control, and the inverter-motor system uses vector control. During simulation, the motor output power and state (traction or braking) can be changed by altering the external torque of the motor. The main circuit (including the power supply, transformer, traction network, converter, and motor) runs in a real-time circuit simulator with a simulation step size of 1µs. The locomotive's control section runs in a real-time digital controller with a sampling frequency of 20kHz.

[0213] Six different power supply distances D were set up in the experiment (increasing from 5km to 30km in 5km increments). Under each operating condition, the locomotive's active power P was varied, and the power factor control was set to lag. The upstream short-circuit capacity of the traction power supply system was set to 1500MVA. The traction transformer parameters are shown in Table 1, with the rail center as the coordinate origin, and the traction network parameters are shown in Table 2. The obtained PV curve simulation results were compared with the theoretical curves, and the average voltage error under each operating condition was statistically analyzed. The results are as follows: Figure 8 As shown in Table 3, it can be seen that the trend of the theoretically calculated curve and the trend of the semi-physical experimental data are very consistent with the changes in the locomotive's active power, with errors only appearing at two extreme points. The average voltage amplitude error under each operating condition does not exceed 0.2kV, and the average relative error does not exceed 0.8%, verifying the accuracy of the first solution substitution formula in the embodiments of this application. Furthermore, during the semi-physical simulation, when the locomotive power reaches near the extreme power, the system experiences voltage collapse and divergence, such as... Figure 9As shown, the accuracy of the limiting power in the extreme point determination formula is proven. Furthermore, it can be seen that as the power supply distance D increases, the limiting power supply of the traction power supply system decreases, but the maximum lifting voltage of the locomotive under regenerative braking increases.

[0214] Table 1 Traction Transformer Parameters

[0215]

[0216] Table 2. Main parameters and locations of each conductor in the direct-supply traction network with single-line return conductor.

[0217]

[0218] Table 3 shows the error between the hardware-in-the-loop simulation results and theoretical calculations of the PV curves of the traction power supply system.

[0219]

[0220] Figure 10 This is a block diagram illustrating a PV curve generation device for a traction power supply system based on regenerative braking, as shown in an exemplary embodiment of this application. Figure 10 As shown, the exemplary PV curve generation device 1000 for a regenerative braking-based traction power supply system includes:

[0221] The first data processing module 1010 is used to construct the locomotive active power expression and the locomotive reactive power expression;

[0222] The second data processing module 1020 is used to determine the feasible solution expression and the infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression;

[0223] The third data processing module 1030 is used to generate PV curves including regenerative braking conditions based on feasible and infeasible solution expressions, with the locomotive active power being less than 0 as the PV curve generation condition, and to generate PV curves including traction conditions with the locomotive active power being greater than 0 as the condition.

[0224] It should be noted that the PV curve generation device for a traction power supply system based on regenerative braking provided in the above embodiments and the PV curve generation method for a traction power supply system based on regenerative braking provided in the above embodiments belong to the same concept. The specific operation methods of each module and unit have been described in detail in the method embodiments and will not be repeated here. In practical applications, the PV curve generation device for a traction power supply system based on regenerative braking provided in the above embodiments can be assigned to different functional modules as needed, that is, the internal structure of the system can be divided into different functional modules to complete all or part of the functions described above. This is not a limitation here.

[0225] Embodiments of this application also provide an electronic device, including: one or more processors; and a storage device for storing one or more programs, which, when executed by one or more processors, cause the electronic device to implement the PV curve generation method for a traction power supply system based on regenerative braking provided in the above embodiments.

[0226] Another aspect of this application provides a computer-readable storage medium storing a computer program thereon, which, when executed by a computer's processor, causes the computer to perform the PV curve generation method for a traction power supply system based on regenerative braking provided in the various embodiments above. This computer-readable storage medium may be included in the electronic device described in the above embodiments, or it may exist independently and not assembled into the electronic device.

[0227] Another aspect of this application provides a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the PV curve generation method for a regenerative braking-based traction power supply system provided in the various embodiments described above.

[0228] In the embodiments of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. The terms "comprising" and "including" as used throughout the specification and claims are open-ended terms and should therefore be interpreted as "comprising but not limited to".

[0229] The above embodiments are merely illustrative of the principles and effects of this application and are not intended to limit this application. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this application. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this application should still be covered by the claims of this application.

Claims

1. A method for generating PV curves in a traction power supply system based on regenerative braking, characterized in that, include: Construct expressions for the locomotive's active power and reactive power; The feasible and infeasible solution expressions are determined based on the locomotive active power expression and the locomotive reactive power expression; Based on feasible and infeasible solution expressions, PV curves including regenerative braking conditions are generated with the locomotive active power being less than 0 as the generation condition, and PV curves including traction conditions are generated with the locomotive active power being greater than 0 as the generation condition.

2. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 1, characterized in that, The expression for the active power of a locomotive includes: ； The expressions for locomotive reactive power include: ； The first intermediate variable expression includes: ； The second intermediate quantity expression includes: ； The third intermediate quantity expression includes: ； in, Indicates active power. Indicates reactive power. This indicates the V / V traction transformer turns ratio. Indicates the first intermediate variable. Indicates the locomotive voltage amplitude. Indicates the second intermediate variable. Indicates the phase voltage amplitude of the power grid source. Indicates the phase angle of the locomotive voltage. Indicates the third intermediate variable. This indicates the resistance of the traction transformer. This represents the resistance per unit length of the T-line. This represents the resistance per unit length of the R-line. This represents the mutual resistance per unit length between the T-line and the R-line. Indicates the distance to the target. Indicates the reactance of the traction transformer. This represents the reactance per unit length of the T-line. This represents the reactance per unit length of the R-line. This represents the mutual reactance per unit length between the T-line and the R-line. This represents the equivalent reactance.

3. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 2, characterized in that, Feasible solution expressions include: ； ； in, This indicates a feasible solution. This represents the first solution. This represents the equivalent resistance calculated based on the power factor. Indicates low-voltage open-circuit voltage. This indicates the intermediate conversion amount.

4. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 3, characterized in that, Based on feasible and infeasible solution expressions, and with the locomotive active power being less than 0 as the PV curve generation condition, PV curves including regenerative braking conditions are generated, including: Determine the equivalent resistance calculated based on the power factor and determine the target conditions based on the equivalent resistance calculated based on the power factor; the target conditions characterize whether there are extreme points in the PV curve of the feasible solution under regenerative braking conditions; Based on the objective conditions and feasible solution expressions, the PV curve is generated with the locomotive active power being less than 0 as the PV curve generation condition, including feasible solutions under regenerative braking conditions. Based on the expression of infeasible solutions, and taking the locomotive's active power being less than 0 as the condition for generating PV curves, PV curves including infeasible solutions under regenerative braking conditions are generated.

5. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 4, characterized in that, The formula for calculating the equivalent resistance based on the power factor is shown below: ； ； in, Indicates the system short-circuit capacity. Indicates the first substitute quantity. Indicates the second substitute quantity. This represents the locomotive power factor.

6. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 4, characterized in that, The target conditions include: When the equivalent resistance calculated by the power factor is less than or equal to 0, the PV curve of the locomotive active power is less than 0 and monotonically increasing in the first interval; the left endpoint of the first interval is the left limit point of the active power of the PV curve, the right endpoint of the first interval is 0, and the first interval is a left-closed and right-open interval. When the equivalent resistance calculated by the power factor is greater than 0, the PV curve of the locomotive active power is less than 0. It is monotonically increasing in the first sub-interval and monotonically decreasing in the second sub-interval. The first interval includes the first sub-interval and the second sub-interval. The first sub-interval and the second sub-interval are obtained according to the extreme point determination formula.

7. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 6, characterized in that, The formulas for determining extreme points include: ； ； ； in, Indicates the extreme point of active power. This indicates the extreme point of the voltage.

8. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 7, characterized in that, The formulas for determining the left limit point of active power include: ； in, This indicates the left limit point of active power.

9. The method for generating PV curves in a traction power supply system based on regenerative braking according to claim 2, characterized in that, Infeasible solution expressions include: ； ； in, Indicates an infeasible solution. This indicates the second solution.

10. A PV curve generation device for a traction power supply system based on regenerative braking, characterized in that, include: The first data processing module is used to construct the locomotive active power expression and the locomotive reactive power expression; The second data processing module is used to determine the feasible solution expression and the infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression. The third data processing module is used to generate PV curves including regenerative braking conditions based on feasible and infeasible solution expressions, with the locomotive active power being less than 0 as the generation condition, and to generate PV curves including traction conditions with the locomotive active power being greater than 0 as the condition.

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