Method and device for generating PV curve of traction power supply system based on regenerative braking

Abstract

The invention provides a method and device for generating a PV curve of a traction power supply system based on regenerative braking, and relates to the technical field of traction power supply system data processing.The method comprises the steps that an active power expression and a reactive power expression of a locomotive are constructed respectively, and a feasible solution expression is determined based on the active power expression of the locomotive; and determining an infeasible solution expression based on the locomotive reactive power expression. The condition that the active power of the locomotive is smaller than 0 is taken as a PV curve generation condition, a PV curve corresponding to a feasible solution under the regenerative braking working condition can be generated based on a feasible solution expression, a PV curve corresponding to an infeasible solution under the regenerative braking working condition can be generated based on an infeasible solution expression, and the feasible solution expression and the infeasible solution expression are equations about the active power of the locomotive. When the PV curve is generated, the PV curve including the regenerative braking working condition can be conveniently and rapidly generated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traction power supply system data processing, in particular to a traction power supply system PV curve generation method and device based on regenerative braking. BACKGROUND

[0002] With the continuous development of the economy in mountainous areas, a large number of mountainous railway in western China is continuously planned. The terrain of high-altitude mountainous railway has a large drop, and the altitude drop in some areas may exceed 3000m. In these areas, long and large slopes are inevitably arranged. When the locomotive climbs uphill, it needs to run at full power, and when it descends, it generally adopts regenerative braking. Regenerative braking refers to the process in which the traction motor converts into a generator during deceleration or descent of the locomotive, generates a braking torque, and feeds back the excess power to the traction network. On long and large slopes, due to the continuous action of gravity, the locomotive is in a regenerative braking state for a long time, continuously feeding power back to the traction network, resulting in negative active power of the locomotive. However, the braking energy will cause the voltage of the traction network to rise, which may cause discharge between the train roof gaps, leading to train braking failure, and when the voltage exceeds 29kV specified in the iron standard, it may cause the train-mounted circuit breaker to trip, affecting the normal operation of the railway. This phenomenon brings a contradiction to the design of the traction power supply system on long and large slopes: when the locomotive climbs uphill, it runs at full power, and the voltage of the traction network decreases, which should be kept as high as possible; when the locomotive descends, it runs in braking mode, and the returned power may cause the voltage of the traction network to rise, which should be kept as low as possible. The existing research has not fully studied the voltage rise characteristics of the locomotive, and the research on the PV curve of the traction power supply system has only stayed in the traction working condition, and has not conducted in-depth research on the PV curve under the regenerative braking working condition. Therefore, studying the voltage rise mechanism of the traction network-locomotive system on long and large slopes has important practical application value for the planning and design of the bus voltage, transformer and traction network parameters of the traction power supply system. SUMMARY

[0003] The present application provides a traction power supply system PV curve generation method and device based on regenerative braking, which can generate a PV curve including a regenerative braking working condition more simply.

[0004] The present application provides a traction power supply system PV curve generation method based on regenerative braking, which comprises: constructing an active power expression of the locomotive and a reactive power expression of the locomotive; determining a feasible solution expression and an infeasible solution expression based on the active power expression of the locomotive and the reactive power expression of the locomotive; based on the feasible solution expression and the infeasible solution expression, generating a PV curve including a regenerative braking working condition with the condition that the active power of the locomotive is less than 0, and generating a PV curve including a traction working condition with the condition that the active power of the locomotive is greater than 0.

[0005] Optionally, the locomotive active power expression includes: ; The locomotive reactive power expression can include: ; The first intermediate variable expression can include: ; The second intermediate variable expression can include: ; The third intermediate variable expression can include: ; wherein, P represents active power, Q represents reactive power, V / v represents a traction transformer turns ratio, V1 represents a first intermediate variable, Vlo represents a locomotive voltage magnitude, V2 represents a second intermediate variable, Vgrid represents a grid supply phase voltage magnitude, θ represents a locomotive voltage phase angle, V3 represents a third intermediate variable, Rt represents a traction transformer resistance, Rt represents a T-line per-unit length resistance, Rr represents a R-line per-unit length resistance, Xt represents a T-line and R-line per-unit length mutual resistance, D represents a target distance, Xt represents a traction transformer reactance, Xt represents a T-line per-unit length reactance, Xr represents a R-line per-unit length reactance, Xt represents a T-line and R-line per-unit length mutual reactance, Xe represents an equivalent reactance.

[0006] Optionally, the feasible solution expression includes: ; ; wherein, S represents a feasible solution, S1 represents a first solution.

[0007] Optionally, based on the feasible solution expression and the infeasible solution expression, generating a PV curve including a regenerative braking operating condition based on a PV curve generation condition that the locomotive active power is less than zero, includes: determining an equivalent resistance of power factor conversion and determining a target condition based on the equivalent resistance of power factor conversion; the target condition represents whether an extreme point exists in a PV curve of a feasible solution under a regenerative braking condition; generating, based on the target condition and the expression of the feasible solution, a PV curve including the feasible solution under the regenerative braking condition, with the PV curve generation condition being that active power of the locomotive is less than 0; generating, based on the expression of the infeasible solution, a PV curve including the infeasible solution under the regenerative braking condition, with the PV curve generation condition being that active power of the locomotive is less than 0.

[0008] Optionally, the calculation formula of the equivalent resistance of power factor conversion is as follows: wherein, represents the equivalent resistance of power factor conversion, represents a low-voltage no-load voltage, represents a system short-circuit capacity, represents a first substitute quantity, represents a second substitute quantity.

[0009] Optionally, the target condition includes: when the equivalent resistance of power factor conversion is less than or equal to 0, the PV curve with active power of the locomotive being less than 0 is monotonically increasing in a first interval; a left end point of the first interval is an active power left limit point of the PV curve, a right end point of the first interval is 0, and the first interval is a left-closed right-open interval; when the equivalent resistance of power factor conversion is greater than 0, the PV curve with active power of the locomotive being less than 0 is monotonically increasing in a first sub-interval and monotonically decreasing in a second sub-interval, and the first interval includes the first sub-interval and the second sub-interval; the first sub-interval and the second sub-interval are determined according to an extreme point determination formula.

[0010] Optionally, the extreme point determination formula includes: wherein, represents an active power extreme point, represents a voltage extreme point, represents the equivalent resistance of power factor conversion, represents the low-voltage no-load voltage, represents an intermediate conversion quantity.

[0011] Optionally, the determination formula of the active power left limit point includes: ;​​​​​ wherein, represents a left active power limit point.

[0012] Optionally, the infeasible solution expression comprises: ; ; wherein, represents an infeasible solution, represents a second solution.

[0013] To achieve the above object and other related objects, the present application provides a PV curve generation device for a regenerative braking based traction power supply system, comprising: a first data processing module configured to construct an active power expression of a locomotive and a reactive power expression of the locomotive; a second data processing module configured to determine an infeasible solution expression and a feasible solution expression based on the active power expression of the locomotive and the reactive power expression of the locomotive; a third data processing module configured to generate a PV curve including a regenerative braking working condition based on the infeasible solution expression and the feasible solution expression with the condition that the active power of the locomotive is less than 0, and generate a PV curve including a traction working condition with the condition that the active power of the locomotive is greater than 0.

[0014] As described above, the PV curve generation method and device for a regenerative braking based traction power supply system provided by the present application have the following beneficial effects: The PV curve generation method for a regenerative braking based traction power supply system provided by the present application constructs an active power expression and a reactive power expression of a locomotive respectively, and determines an infeasible solution expression based on the active power expression of the locomotive and a feasible solution expression based on the reactive power expression of the locomotive. With the condition that the active power of the locomotive is less than 0, the PV curve generation method can generate a PV curve corresponding to a feasible solution under a regenerative braking working condition based on the feasible solution expression, and generate a PV curve corresponding to an infeasible solution under the regenerative braking working condition based on the infeasible solution expression. The feasible solution expression and the infeasible solution expression are equations about the active power of the locomotive, and thus the PV curve generation method can facilitate the generation of the PV curve including the regenerative braking working condition.

[0015] It should be understood that the general description above and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS

[0016] The accompanying drawings, which are incorporated into and constitute a part of this specification, illustrate preferred embodiments of the present application and, together with the description, serve to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained from these drawings without creative labor for those skilled in the art. In the drawings: Figure 1 is a flow chart of a method for generating a PV curve of a regenerative braking based traction power supply system according to an exemplary embodiment of the present application; Figure 2 is a schematic diagram of a structure of a direct power supply mode traction power supply system with a return line; Figure 3 is a schematic diagram of a cross-section structure of a direct power supply traction network; Figure 4 is a schematic diagram of an equivalent circuit of a high-level three-phase power grid-traction power supply-locomotive; Figure 5 is a locomotive voltage PV curve considering regenerative braking power; Figure 6 is a hardware-in-the-loop semi-physical simulation platform; Figure 7 is a schematic diagram of a structure of a hardware-in-the-loop experimental system; Figure 8 is a comparison diagram of a semi-physical simulation result of a traction power supply system PV curve and a theoretical curve; Figure 9 is a semi-physical limit simulation curve of a traction power supply system PV curve; Figure 10 is a structure block diagram of a PV curve generating device of a regenerative braking based traction power supply system according to an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0017] The embodiments of the present application will be described hereinafter with reference to the accompanying drawings and preferred embodiments, and other advantages and effects of the present application can be easily understood by those skilled in the art from the contents disclosed in the present specification. The present application can also be implemented or applied in other different specific embodiments, and various modifications or changes can be made to the details of the present specification based on different views and applications without departing from the spirit of the present application. It should be understood that the preferred embodiments are only for illustrating the present application, but not for limiting the protection scope of the present application.

[0018] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner, and only the components related to the present application are shown in the diagrams, but not drawn according to the number, shape and size of the components in actual implementation, and the type, number and proportion of each component in actual implementation can be arbitrarily changed, and the component layout type can also be more complex.

[0019] In the following description, numerous specific details are discussed in order to provide a thorough understanding of the embodiments of the application. However, it will be apparent to one skilled in the art that the embodiments of the application can be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the embodiments of the application.

[0020] Referring to Figure 1 , Figure 1 is a flow chart of a method for generating a PV curve of a regenerative braking based traction power supply system according to an exemplary embodiment of the application. Referring to Figure 1 It can be seen that the method for generating a PV curve of a regenerative braking based traction power supply system can comprise: Step S110, constructing an active power expression and a reactive power expression of a locomotive.

[0021] In an embodiment of the application, an active power expression and a reactive power expression of a locomotive can be constructed.

[0022] A traction substation, also known as a traction substation, is a facility that can convert high voltage power from a local power grid into single-phase AC power suitable for use by electric locomotives. A bus is a conductor inside the traction substation that collects and distributes electrical energy. The distance of the locomotive from the traction substation bus can be the electrical distance of the locomotive along the railway line to the traction substation that supplies it. The locomotive voltage amplitude is a function of two variables, locomotive power and supply distance, and after the target distance (distance of the locomotive from the traction substation bus) is fixed, the locomotive voltage amplitude can be obtained based on the active power and the reactive power of the locomotive.

[0023] Exemplarily, when simulating and solving the PV curve under the regenerative braking condition before the actual operation of the locomotive, the target distance can be set by the user.

[0024] Exemplarily, the active power expression of the locomotive can include: ; The reactive power expression of the locomotive can include: ; The first intermediate variable expression can include: ; The second intermediate variable expression can include: ; The third intermediate variable expression can include: ; wherein, represents the active power, represents the 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.

[0025] 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 line impedance per unit length. 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.

[0026] Based on the voltage relationship between the high and low voltage sides of the traction transformer, the first expression can be obtained: ; in, express Figure 4 The voltage at midpoint 3, express Figure 4 The voltage at midpoint 4, express Figure 4 Voltage at midpoint 5.

[0027] Based on the relationship between the high and low voltage sides of the traction transformer, the second expression can be obtained: ; in, expressFigure 4 The current at midpoint 1, express Figure 4 The current at midpoint 7, express Figure 4 The current at midpoint 2.

[0028] 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: ; The fourth expression can be represented as: ; in, express Figure 4 The voltage at midpoint 1, Represents the imaginary part of a complex number. express Figure 4 Voltage at midpoint 2.

[0029] Substituting the third and fourth expressions into the first expression, we get the fifth expression: .

[0030] 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: ; The seventh expression can be represented as: ; 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.

[0031] Substituting the sixth and seventh expressions into the fifth expression, we obtain the eighth expression: .

[0032] Assuming the upper grid is symmetrical, the ninth expression can be obtained: .

[0033] Substitute the ninth expression into the eighth expression and take the conjugate, the tenth expression can be obtained: ; wherein, represents Figure 4 the conjugate complex of the current at the midpoint 7.

[0034] The expression of the complex power of the locomotive can be expressed as: ; wherein, represents the active power, represents the reactive power.

[0035] Based on the expression of the complex power of the locomotive, the active power expression and the reactive power expression of the locomotive can be obtained.

[0036] Step S120, determine the feasible solution expression and the infeasible solution expression based on the active power expression and the reactive power expression of the locomotive.

[0037] In an embodiment of the present application, the feasible solution expression and the infeasible solution expression can be obtained by performing algebraic operations on the active power expression and the reactive power expression of the locomotive.

[0038] Alternatively, the active power expression and the reactive power expression of the locomotive can be moved and squared and then added to obtain a first solving expression, which can be expressed as: ; Substitute the square of the amplitude of the locomotive voltage to obtain a second solving expression, which can be expressed as: ; wherein, , is a replacement quantity; Based on the second solving expression, the feasible solution expression and the infeasible solution expression are obtained.

[0039] The feasible solution expression can include: ; ; The infeasible solution expression can include: ; ; wherein, represents a feasible solution, represents an infeasible solution, represents a first solution, represents a second solution.

[0040] It should be noted that the feasible solution can also be referred to as a high-pressure solution, which is a stable equilibrium point of the system. The infeasible solution can also be referred to as a low-pressure solution, which is an unstable equilibrium point of the system.

[0041] In step S130, based on the feasible solution expression and the infeasible solution expression, a PV curve including a regenerative braking working condition is generated under the condition that the locomotive active power is less than 0, and a PV curve including a traction working condition is generated under the condition that the locomotive active power is greater than 0.

[0042] wherein, the locomotive active power less than 0 represents the regenerative braking working condition, and the locomotive active power greater than 0 represents the traction working condition.

[0043] In an embodiment of the present application, after obtaining the feasible solution expression and the infeasible solution expression, a PV curve including a regenerative braking working condition can be generated based on the feasible solution expression and the infeasible solution expression under the condition that the locomotive active power is less than 0, and / or a PV curve including a traction working condition can be generated based on the feasible solution expression and the infeasible solution expression under the condition that the locomotive active power is greater than 0. That is, a PV curve including a regenerative braking working condition can be generated based on the feasible solution expression and the infeasible solution expression under the condition that the locomotive active power is less than 0; a PV curve including a traction working condition can be generated based on the feasible solution expression and the infeasible solution expression under the condition that the locomotive active power is greater than 0; and a PV curve including a regenerative braking working condition and a traction working condition can be generated based on the feasible solution expression and the infeasible solution expression under the condition that the locomotive active power is less than 0 and the locomotive active power is greater than 0.

[0044] Based on the above feasible solution expression and the infeasible solution expression, it can be found that the locomotive voltage amplitude is a function of the locomotive active power and the target distance, that is: ; If the variable target distance is fixed, the relationship between the locomotive active power and the locomotive voltage amplitude, that is, the PV curve, can be obtained.

[0045] It should be noted that in the process of obtaining the PV curve based on the feasible solution expression and the infeasible solution expression, under the premise of fixing the target distance, since the locomotive active power value can be directly set into the feasible solution expression or the infeasible solution expression to obtain the locomotive voltage amplitude, the solving process of the PV curve can be simplified, the effect of fast solving is achieved, and the generation efficiency of the PV curve is improved.

[0046] Optionally, in the process of generating the PV curve including the regenerative braking working condition based on the feasible solution expression and the infeasible solution expression with the condition that the locomotive active power is less than 0 in step S140, the process can include steps S131 to S133.

[0047] In step S131, the equivalent resistance converted by the power factor is determined, and the target condition is determined based on the equivalent resistance converted by the power factor.

[0048] The target condition represents whether the PV curve of the feasible solution in the regenerative braking working condition has an extreme point.

[0049] The target condition can include: When the equivalent resistance converted by the power factor is less than or equal to 0, the PV curve with the locomotive active power less than 0 is monotonically increasing in the first interval; the left end point of the first interval is the active power left limit point of the PV curve, the right end point of the first interval is 0, and the first interval is a left-closed right-open interval. When the equivalent resistance converted by the power factor is greater than 0, the PV curve with the locomotive active power less than 0 is monotonically increasing in the first sub-interval and monotonically decreasing in the second sub-interval, and 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.

[0050] In the process of solving the PV curve, the simulation parameters such as the locomotive active power and the power factor need to be set by the operator in advance, and the locomotive reactive power can be determined based on the power factor and the locomotive active power.

[0051] For example, when the power factor lags, the locomotive reactive power expression is as follows: ; Wherein, represents the locomotive power factor.

[0052] For example, when the power factor leads, the locomotive reactive power expression is as follows: ; The system short-circuit capacity can be set as The system short-circuit capacity and the equivalent reactance have the following relationship: ; The equivalent reactance determination formula can be expressed as: ; wherein, represents the system short-circuit capacity, represents the equivalent reactance, represents the grid power supply phase voltage amplitude.

[0053] The low-voltage no-load voltage expression can be expressed as: ; wherein, represents the low-voltage no-load voltage.

[0054] The first solution replacement formula can be obtained by substituting the locomotive reactive power, the equivalent reactance determination formula, the low-voltage side no-load voltage, the second intermediate quantity expression, and the third intermediate quantity expression into the expression of the first solution in the feasible solution expression when the power factor lags. The first solution replacement formula can be expressed as: ; wherein, represents the power factor conversion equivalent resistance, represents the intermediate conversion quantity.

[0055] The power factor conversion equivalent resistance can be expressed as: ; The intermediate conversion quantity can be expressed as: ; wherein, the first substitute quantity and the second substitute quantity can be expressed as: ; wherein, represents the first substitute quantity, represents the second substitute quantity.

[0056] The first solution replacement formula can be obtained by substituting the locomotive reactive power, the equivalent reactance determination formula, the low-voltage side no-load voltage, the second intermediate quantity expression, and the third intermediate quantity expression into the expression of the first solution in the feasible solution expression when the power factor leads. The first solution replacement formula can be expressed as: ; wherein, represents the power factor conversion equivalent resistance, represents the intermediate conversion quantity.

[0057] The power factor conversion equivalent resistance can be expressed as: ; The intermediate conversion quantity can be expressed as: ; wherein the first and second surrogates can be expressed as: ; wherein, represents the first surrogate, represents the second surrogate.

[0058] For example, analyzing the first solution expression, since represents the square of the locomotive voltage amplitude, thus is a non-negative real number, thus it is necessary to examine the intermediate equation in the first solution substitution formula: ; The intermediate equation is a quadratic equation in , and the discriminant of its roots is: ; Then the two roots of the intermediate equation are: ; In order to ensure that has a real solution, it is necessary to ensure that .

[0059] and are the left and right limit points of the PV curve. In traditional power systems, only the right positive power limit point P2 is concerned, and the left negative power limit point P1 is rarely concerned.

[0060] When the locomotive is in regenerative braking operation, i.e. P<0, the derivative of active power P is obtained by using the first solution substitution formula, and the derivative is equal to 0, which can obtain the active power derivative formula: ; Then the above formula can be further simplified as: ; Since , it can be analyzed that whether the simplified active power derivative formula has a solution depends on the positive and negative of the equivalent resistance of the power factor conversion. Therefore, it is necessary to discuss according to the lead and lag of the power factor.

[0061] When the locomotive power factor lags, P<0 in regenerative braking operation, the expression of the equivalent resistance of the power factor conversion is: ; 1) If , the simplified active power derivative formula has no solution, and the active power derivative formula , which indicates that the first solution is monotonically increasing on the interval [P1, 0); 2) If , the simplified active power derivative formula has a unique negative solution: . and . The above analysis shows that when there is a negative real number of active power on the PV curve that can make the locomotive voltage rise to a maximum value. Substituting the unique negative solution of the simplified active power derivative formula into the feasible solution expression can obtain the maximum value as: . In addition, when , there is , which indicates that is monotonically increasing on the interval , that is, is monotonically increasing on the first interval. When , there is , which indicates that is monotonically decreasing on the interval , that is, is monotonically decreasing on the second interval.

[0062] Step S132, based on the target condition and the feasible solution expression, a PV curve generation condition that the active power of the locomotive is less than 0 is used to generate a PV curve including feasible solutions under regenerative braking conditions.

[0063] In an embodiment of the present application, based on the target condition and the feasible solution expression, a PV curve generation condition that the active power of the locomotive is less than 0 can be used to generate a PV curve including feasible solutions under regenerative braking conditions.

[0064] Based on the analysis of step S131, the PV curve of the locomotive voltage can be plotted, and according to the positive and negative of , the PV curve can be divided into two groups: (1) When , the PV curve is as shown in Figure 5 (a) and Figure 5(b) shown. As can be seen from 5(a), the whole PV curve can be composed of two parts, the red curve corresponds to the feasible solution, and the blue curve corresponds to the infeasible solution. As can be seen from 5(b), the whole PV curve can also be composed of two curves. The left orange curve represents the PV curve of the locomotive regenerative braking condition, and the right green curve represents the PV curve of the locomotive traction condition. It can be seen that in this case, the PV curve under regenerative braking and the PV curve under traction condition have similar rules, that is, the voltage gradually decreases with the increase of power, and there is a limit power (P1 under regenerative braking condition and P2 under traction condition).

[0065] (2) When , the PV curve is shown in 5(c) and (d). It can be found that in this case, the PV curve under regenerative braking condition and the PV curve under traction condition have different change rules. Under regenerative braking condition, with the increase of braking power, the voltage of the locomotive first increases and then decreases, and there is a limit voltage . This shows that the greater the braking power, the greater the voltage of the locomotive. When the braking power of the locomotive is greater than , the voltage of the locomotive will decrease instead, and there will be a limit braking power . Because too high voltage of the locomotive will cause traction blocking or power reduction operation, according to the standard, the voltage of the locomotive should not exceed 29kV. This makes the traction power supply system distributed on the long and large slope must consider the control of the bus voltage on the low voltage side of the traction transformer. If the bus voltage is set too high, it is easy to cause the voltage of the locomotive to exceed the upper limit, and if the bus voltage is set too low, it is easy to cause the traction network voltage to exceed the lower limit. Therefore, the proposed PV curve formula of the locomotive can provide theoretical support for the design of the traction network bus voltage on the long and large slope.

[0066] It should be pointed out that the power factor of the locomotive is generally between -0.95 and -1 under regenerative braking condition, so in most cases, only the case in 5(c) will occur.

[0067] When the power factor of the locomotive is leading, the following formula exists: ; At this time, , the case is similar to the case (2) of the lagging power factor of the locomotive. That is, there is a negative real active power PMP on the PV curve that can make the voltage of the locomotive reach the maximum value, and the PV curve is shown in 5(c) and (d), and there is no monotonic decreasing case as in 5(a) and (b).

[0068] In step S133, based on the infeasible solution expression, the PV curve including the infeasible solution under regenerative braking condition is generated with the condition that the active power of the locomotive is less than 0.

[0069] In one embodiment of the present application, the PV curve including infeasible solutions in regenerative braking operating conditions can be generated based on infeasible solution expressions, with the condition that the locomotive active power is less than 0.

[0070] After obtaining the PV curve, the vertex (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 collapse sharply. By analyzing the distance of the current operating point from the vertex, the voltage stability margin of the system can be evaluated.

[0071] To verify the accuracy of the locomotive voltage PV curve, an example is built as shown in Figure 6 The hardware-in-the-loop semi-physical simulation platform includes a real-time circuit simulator (NI PXIe-FPGA-7868R) based on FPGA, which can simulate various power supplies, different power grid types and different IGBT topologies, etc. The real-time digital controller (NI PXIe-8821-7846R) is a fast control prototype-based actual industrial controller responsible for running the control algorithm, collecting circuit voltage and current, and outputting digital control signals. The I / O board card is responsible for the analog / digital signal connection between the real-time circuit simulator and the controller. The oscilloscope displays various voltage and current waveforms during system operation. The host equipped with StarSim software can display, record and save all data during system operation.

[0072] The structure of the hardware-in-the-loop experimental system is shown in Figure 7 It is composed of a three-phase power supply, a V / v traction transformer, a sub-traction network 1, a sub-traction network 2 and an AC / DC / AC locomotive. The lengths of the sub-traction network 1 and the sub-traction network 2 can be arbitrarily changed, thereby simulating the relative motion of 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 changing the motor external torque. The main circuit (including power supply, transformer, traction network, converter and motor) runs in the real-time circuit simulator with a simulation step of 1us. The control part of the locomotive runs in the real-time digital controller with a sampling frequency of 20kHz.

[0073] Six different power supply distances D are set in the experiment (from 5km to 30km, with an increase interval of 5km). In each operating condition, the locomotive active power P is changed, and the power factor control is lagging. The upper short-circuit capacity of the traction power supply system is set to 1500MVA. The traction transformer parameters are shown in Table 1, and the traction network parameters are shown in Table 2, with the track center as the coordinate origin. The obtained PV curve simulation results are compared with the theoretical curve, and the voltage average error under each operating condition is calculated, and the results are shown in Figure 8and Table 3. It can be seen that the trend of the theoretical calculation curve is consistent with the trend of the semi-physical experiment data, and only errors occur at two extreme points. The average error of the voltage amplitude is not more than 0.2 kV, and the average relative error is not more than 0.8% under each working condition, verifying the accuracy of the first solution replacement formula in the embodiment of the present application. Further, in the semi-physical simulation process, when the locomotive power reaches the vicinity of the limit power, the system appears voltage collapse and divergence, as shown in Figure 9 . The accuracy of the limit power in the extreme point determination formula is proved. In addition, it can be seen from Table 3 that, as the power supply distance D increases, the limit power supply power of the traction power supply system is decreasing, but the maximum lifting voltage of the locomotive under regenerative braking is increasing.

[0074] Table 1 Traction transformer parameters Table 2 Main parameters and positions of each conductor of the direct supply traction network with a return wire Table 3 Error of semi-physical simulation results and theoretical calculation of the PV curve of the traction power supply system Figure 10 is a block diagram of a regenerative braking-based traction power supply system PV curve generation device according to an example embodiment of the present application. As shown in Figure 10 , the example regenerative braking-based traction power supply system PV curve generation device 1000 includes: a first data processing module 1010, configured to construct a locomotive active power expression and a locomotive reactive power expression; a second data processing module 1020, configured to determine a feasible solution expression and an infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression; a third data processing module 1030, configured to generate a PV curve including a regenerative braking working condition based on the feasible solution expression and the infeasible solution expression, and generate a PV curve including a traction working condition based on the condition that the locomotive active power is greater than 0.

[0075] It should be noted that the apparatus for generating a PV curve of a regenerative braking based traction power supply system provided in the above embodiments and the method for generating a PV curve of a regenerative braking based traction power supply system provided in the above embodiments belong to the same concept, and the specific manner in which each module and unit performs operations has been described in detail in the method embodiments, which will not be repeated here. The apparatus for generating a PV curve of a regenerative braking based traction power supply system provided in the above embodiments can be applied in actual application, and the above functions can be completed by different functional modules according to needs, that is, the internal structure of the system is divided into different functional modules to complete all or part of the functions described above, and this is not limited herein.

[0076] Embodiments of the present application also provide an electronic device, comprising: one or more processors; a storage device for storing one or more programs, which, when executed by the one or more processors, cause the electronic device to implement the method for generating a PV curve of a regenerative braking based traction power supply system provided in each of the above embodiments.

[0077] Another aspect of the present application also provides a computer readable storage medium having a computer program stored thereon, which, when executed by a processor of a computer, causes the computer to perform the method for generating a PV curve of a regenerative braking based traction power supply system provided in each of the above embodiments. The computer readable storage medium can be included in the electronic device described in the above embodiments, or can exist separately and not be assembled into the electronic device.

[0078] Another aspect of the present application also provides a computer program product or a computer program, which comprises 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 the processor executes the computer instructions, so that the computer device performs the method for generating a PV curve of a regenerative braking based traction power supply system provided in each of the above embodiments.

[0079] In the embodiments of the present application, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood or implied to indicate or suggest relative importance. "Include" and "comprise" mentioned throughout the specification and claims are open terms, and should be interpreted as "including but not limited to".

[0080] The above embodiments only exemplarily illustrate the principles and effects of the present application, and are not used to limit the present application. Any person skilled in the art can modify or change the above embodiments without departing from the spirit and scope of the present application. Therefore, all equivalent modifications or changes made by those skilled in the art without departing from the spirit and technical thought of the present application should be covered by the claims of the present application.

Claims

1. A method for generating a PV curve of a regenerative braking based traction power supply system, characterized in that, The method comprises the following steps: constructing locomotive active power expression and locomotive reactive power expression; determining feasible solution expression and infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression; generating PV curve including regenerative braking working condition based on the condition that the locomotive active power is less than 0 and generating PV curve including traction working condition based on the condition that the locomotive active power is greater than 0.

2. The regenerative braking based traction power supply system PV curve generation method of claim 1, wherein, The locomotive active power expression comprises: ； The locomotive reactive power expression can comprise: ； The first intermediate variable expression can comprise: ； The second intermediate variable expression can comprise: ； The third intermediate variable expression can comprise: ； wherein, represents active power, represents reactive power, represents V / v traction transformer ratio, represents a first intermediate variable, represents locomotive voltage magnitude, represents a second intermediate variable, represents grid supply phase voltage magnitude, represents locomotive voltage phase angle, represents a third intermediate variable, represents traction transformer resistance, represents T-line per-unit length resistance, represents R-line per-unit length resistance, represents T-line and R-line per-unit length mutual resistance, represents target distance, represents traction transformer reactance, represents T-line per-unit length reactance, represents R-line per-unit length reactance, represents T-line and R-line per-unit length mutual reactance, represents equivalent reactance.

3. The method of claim 1, wherein the PV curve is generated based on a regenerative braking force of the vehicle. The feasible solution expression comprises: ； ； wherein, denotes a feasible solution, denotes a first solution.

4. The regenerative braking based traction power supply system PV curve generation method of claim 1, wherein, The PV curve including the regenerative braking working condition is generated based on the condition that the locomotive active power is less than 0 and the infeasible solution expression, and the PV curve including the traction working condition is generated based on the condition that the locomotive active power is greater than 0 and the feasible solution expression. determining the equivalent resistance converted by the power factor and determining the target condition based on the equivalent resistance converted by the power factor; the target condition represents whether there is an extreme point of the PV curve of the feasible solution under the regenerative braking working condition; the PV curve including the regenerative braking working condition of the feasible solution is generated based on the condition that the locomotive active power is less than 0 and the target condition; the PV curve including the regenerative braking working condition of the infeasible solution is generated based on the condition that the locomotive active power is less than 0 and the infeasible solution expression.

5. The regenerative braking based traction power supply system PV curve generation method of claim 4, wherein, The calculation formula of the equivalent resistance converted by the power factor is as follows: ； ； wherein, represents the equivalent resistance of the power factor conversion, represents the low-voltage no-load voltage, represents the system short-circuit capacity, represents the first substitute amount, represents the second substitute amount.

6. The regenerative braking based traction power supply system PV curve generation method of claim 4, wherein, The target condition comprises: when the equivalent resistance converted by the power factor is less than or equal to 0, the PV curve of the locomotive active power less than 0 is monotonically increasing in the first interval; the left end point of the first interval is the active power left limit point of the PV curve, the right end point of the first interval is 0, and the first interval is a left-closed right-open interval; when the equivalent resistance converted by the power factor is greater than 0, the PV curve of the locomotive active power less than 0 is monotonically increasing in the first sub-interval and monotonically decreasing in the second sub-interval, and the first interval comprises 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 regenerative braking based traction power supply system PV curve generation method of claim 6, wherein, The extreme point determination formula comprises: ； ； ； wherein, denotes the active power extremum point, denotes the voltage extremum point, denotes the power factor reduced equivalent resistance, denotes the low voltage no-load voltage, denotes the intermediate reduced quantity.

8. The regenerative braking based traction power supply system PV curve generation method of claim 7, wherein, The determination formula of the active power left limit point comprises: ； wherein, represents the active power left limit point.

9. The regenerative braking based traction power supply system PV curve generation method of claim 1, wherein, The infeasible solution expression comprises: ； ； wherein, denotes an infeasible solution, denotes a second solution.

10. A device for generating a PV curve of a regenerative braking based traction power supply system, characterized in that The method comprises the following steps: The first data processing module is configured to construct locomotive active power expression and locomotive reactive power expression; The second data processing module is configured to determine feasible solution expression and infeasible solution expression based on the locomotive active power expression and the locomotive reactive power expression; The third data processing module is configured to generate PV curve including regenerative braking working condition based on the condition that the locomotive active power is less than 0 and generate PV curve including traction working condition based on the condition that the locomotive active power is greater than 0.

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