Converter station no-load closing strategy making method based on inrush current-free closing angle interval

Abstract

The invention relates to a converter station no-load closing strategy making method based on an inrush current-free closing angle interval, and belongs to the technical field of power systems. The method comprises the following steps: firstly, integrating a voltage waveform to obtain residual magnetism of each phase converter transformer, and determining a three-phase switching-on sequence based on the residual magnetism; then calculating an ideal closing angle and a non-inrush current interval of the first closing phase according to the residual magnetism of the first closing phase and the closing resistance input time, and selecting a closing angle of the first closing phase in the non-inrush current interval based on the action dispersion of the circuit breaker; and finally, calculating an ideal closing angle and a non-inrush current interval of the second closing phase according to the residual magnetism of the second closing phase and the closing resistance input time, and selecting a closing angle of the second closing phase in the non-inrush current interval according to the action dispersion of the circuit breaker. According to the invention, the excitation inrush current can be effectively suppressed when the motion dispersibility of the circuit breaker is relatively high.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems and relates to a method for formulating a no-inrush closing strategy for a converter station based on the no-inrush closing angle interval. Background Art

[0002] A converter station is a core component in a DC power transmission system. When changing the transmitted power, the switching of converter transformers needs to be carried out. When a converter transformer is closed with no load, if the three-phase circuit breaker is closed without considering the residual magnetism before closing and the connection method, the iron core may be deeply saturated after closing, generating an exciting inrush current with large amplitude, complex harmonic content, and slow attenuation, which may lead to maloperation of protection, deterioration of voltage quality, burning of filters, etc., seriously threatening the stable operation of the DC power transmission system.

[0003] Therefore, a phase-selection closing device and a closing resistor are equipped in a conventional DC power transmission converter station to suppress the exciting inrush current. In engineering practice, due to the influence of factors such as control signal deviation and mechanical action delay, the action of the circuit breaker has dispersion, and there is often a deviation between the actual closing angle and the preset closing angle. If the dispersion is large, a relatively large-amplitude exciting inrush current will still be generated.

[0004] Existing no-load closing strategies for converter transformers do not slightly correct the closing angle by considering the influence of the closing resistor on the flux linkage waveform on the basis of phase-selection closing, lack the analysis of the transient process of the closing resistor switching, and do not fully quantify the inhibitory effect of the closing resistor on the exciting inrush current. Therefore, when the deviation of the closing angle is large, a huge exciting inrush current may be generated. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for formulating a no-inrush closing strategy for a converter station based on the no-inrush closing angle interval, which can determine the closing angle range without generating an exciting inrush current according to the inhibitory effect of the closing resistor on the exciting inrush current when determining the closing resistor input time. On this basis, adjusting the closing angle can achieve complete suppression of the exciting inrush current under the condition of large dispersion of the circuit breaker action, ensuring the successful commissioning of the converter transformer.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] A method for formulating a no-inrush closing strategy for a converter station based on the no-inrush closing angle interval, which calculates the no-inrush closing angle interval of each phase during three-phase asynchronous closing according to the topological structure of the converter station and the residual magnetism of the three-phase converter transformer. The method specifically includes the following steps:

[0008] S1: Obtain the voltage waveforms when the three-phase converter transformer is switched off and the closing resistor input time;

[0009] S2: Calculate and obtain the residual magnetism of the three-phase commutation transformer according to the voltage waveform when the commutation transformer switches off.

[0010] S3: Determine the closing sequence of the three phases according to the magnitude and direction of the residual magnetism of the three-phase commutation transformer.

[0011] S4: Determine the ideal no-load closing angle and the no-inrush closing angle interval of the first closing phase according to the residual magnetism of the first closing phase and the input time of the closing resistor.

[0012] S5: Select the closing angle of the first closing phase within the no-inrush closing angle interval of the first closing phase according to the dispersion of the breaker operation, and ensure that the actual closing angle of the breaker is within the interval as much as possible.

[0013] S6: Determine the ideal no-load closing angle and the no-inrush closing angle interval of the second closing phase according to the selected closing angle of the first closing phase, the residual magnetism of the first closing phase, and the input time of the closing resistor.

[0014] S7: Select the closing angle of the second closing phase within the no-inrush closing angle interval of the second closing phase according to the dispersion of the breaker operation, and ensure that the actual closing angle of the breaker is within the interval as much as possible.

[0015] Furthermore, in step S2, the calculation formula for the residual magnetism of the three-phase commutation transformer is:

[0016]

[0017] where t1 is the lower limit of voltage integration, t2 is the upper limit of voltage integration, ψ r_x is the residual magnetism after the x-phase commutation transformer switches off, u x (t) is the voltage curve of the x-phase commutation transformer, and x is one of phase A, phase B, and phase C.

[0018] Furthermore, in step S3, the method for determining the closing sequence of the three phases is divided into the following steps:

[0019] S31: Select the phase with the largest absolute value of residual magnetism as the first closing phase.

[0020] S32: Select the phase leading the first closing phase by 120° as the second closing phase.

[0021] Furthermore, in step S4, the calculation formula for the ideal no-load closing angle of the first closing phase is:

[0022]

[0023] where θ fir_1 is the ideal no-load closing angle of the first closing phase, ψ r_fir is the residual magnetism after the first closing phase commutation transformer switches off, ψ mis the peak value of the magnetic flux during the rated operation of the converter transformer.

[0024] Further, in step S4, the no-inrush closing angle interval of the first closing phase is [θ b_fir , θ fir_1 , where θ b_fir is the closing angle at which the closing resistor of the first closing phase completely suppresses the inrush current, and the expression is:

[0025]

[0026] where T is the input time of the closing resistor; ψ dc_fir is the transient component of the magnetic flux of the first closing phase after closing, and the expression is:

[0027] ψ dc_fir = -ψ m cosθ fir + ψ r_fir

[0028] where θ fir is the actual closing angle of the first closing phase.

[0029] Further, in step S6, the calculation formula for the ideal no-load closing angle of the second closing phase is:

[0030]

[0031] where θ sec_1 is the ideal no-load closing angle of the second closing phase, ψ dc_sec is the transient component of the magnetic flux of the second closing phase after closing; ψ m is the peak value of the magnetic flux during the rated operation of the converter transformer, and α sec is the initial phase of the second closing phase.

[0032] Further, step S5 specifically includes: assuming that the action dispersions of the circuit breakers of each phase in advance and lag are the same, and selecting the midpoint of the no-inrush closing angle interval as the actual closing angle of the first closing phase, that is:

[0033] Further, in step S6, the no-inrush closing angle interval of the second closing phase is [θ b_sec , θ sec_1 , where θ b_sec is the closing angle at which the closing resistor of the second closing phase completely suppresses the inrush current;

[0034]

[0035] where T is the input time of the closing resistor; ψ dc_sec is the transient component of the magnetic flux of the second closing phase after closing, and the expression is:

[0036]

[0037] where θ fir is the actual closing angle of the first closing phase, and θ b_fir is the closing angle at which the closing resistor of the first closing phase completely suppresses the inrush current; ψ r_x is the residual magnetism after the circuit breaker of phase x is opened, and x is one of phase A, phase B, and phase C; ψ s is the knee point of the magnetic flux;

[0038] θ a_fir is the closing angle at which the closing resistor of the first closing phase has an inhibitory effect on the inrush current, and the expression is:

[0039]

[0040] Further, step S7 specifically includes: assuming that the action dispersions of the circuit breakers of each phase in advance and lag are the same, selecting the midpoint of the no-inrush current closing angle interval as the closing angle of the second closing phase, and closing the remaining two phases simultaneously after the first closing phase has been closed for one cycle.

[0041] The beneficial effects of the present invention are as follows: The method for formulating the no-load closing strategy of a conventional HVDC converter station based on the no-inrush current closing angle interval provided by the present invention first integrates the voltage waveform to obtain the residual magnetism of each phase of the converter transformer and determines the three-phase closing sequence based on the residual magnetism; then calculates the ideal closing angle and the no-inrush current interval of the first closing phase according to the residual magnetism of the first closing phase and the closing resistor input time, and selects the closing angle of the first closing phase within the no-inrush current interval based on the circuit breaker action dispersion; finally calculates the ideal closing angle and the no-inrush current interval of the second closing phase according to the residual magnetism of the second closing phase and the closing resistor input time, and selects the closing angle of the second closing phase within the no-inrush current interval according to the circuit breaker action dispersion. This method can determine the closing angle range without generating inrush current according to the inhibitory effect of the closing resistor on the inrush current when the closing resistor input time is determined, and can effectively suppress the inrush current when the circuit breaker action dispersion is large, ensuring the successful no-load commissioning of the converter transformer.

[0042] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0043] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0044] Figure 1 Flow chart of the no-inrush closing angle interval-based no-load closing strategy formulation method for the conventional HVDC converter station provided by the present invention;

[0045] Figure 2 No-load closing simulation model of 6 single-phase converter transformers at one end;

[0046] Figure 3 Peak magnetizing inrush current under different closing angles and closing resistor insertion times;

[0047] Figure 4 Peak magnetizing inrush current under different closing angles and residual magnetism;

[0048] Figure 5 Peak inrush current generated by closing using the method of the present invention under different opening angles;

[0049] Figure 6 Peak magnetizing inrush current under different breaker operation dispersions. Detailed implementation manners

[0050] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0051] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and should not be construed as limiting the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, and do not represent the dimensions of actual products; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0052] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, it is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0053] Please refer to Figures 1 to 6 , in order to illustrate the implementation method of the present invention and verify the effectiveness of the said method, a no-load closing simulation model of 6 single-phase converter transformers at one end as shown in Figure 2 is built with reference to the on-site converter station structure and device parameters, and multiple in-operation - opening - closing simulation experiments are carried out. When closing, the closing strategy is formulated according to the method in this article. An embodiment of the present invention proposes a method for formulating a no-load closing strategy for a conventional HVDC converter station based on the no-inrush closing angle interval. As shown in Figure 1 , it includes the following steps:

[0054] (1) Obtain the voltage waveforms at the time of opening of the three-phase converter transformer and the closing resistor input time;

[0055] (2) Calculate and obtain the residual magnetism of the three-phase converter transformer according to the voltage waveforms at the time of opening of the converter transformer;

[0056] (3) Determine the closing sequence of the three phases according to the magnitude and direction of the residual magnetism of the three-phase converter transformer;

[0057] (4) Determine the ideal no-load closing angle and the no-inrush closing angle interval of the first closing phase according to the residual magnetism of the first closing phase and the closing resistor input time;

[0058] (5) Select the closing angle of the first closing phase within the no-inrush closing angle interval of the first closing phase according to the dispersion of the breaker operation, and try to ensure that the actual closing angle of the breaker is within the interval;

[0059] (6) Determine the ideal no-load closing angle and the no-inrush closing angle interval of the remaining closing phases according to the selected closing angle of the first closing phase, the residual magnetism of the first closing phase and the closing resistor input time;

[0060] (7) Select the closing angle of the second closing phase within the no-inrush closing angle interval of the second closing phase according to the dispersion of the breaker operation, and try to ensure that the actual closing angle of the breaker is within the interval.

[0061] Since the closing resistor input time in the project is generally 8 - 11 ms, in order to simulate the closing resistor, the closing resistor input time T in step (1) of this embodiment takes 8 ms.

[0062] After reading the voltage waveforms of the transformer after opening in the simulation software, according to step (2), the residual magnetism of the three phases is calculated by using the method of voltage integration. The formula is:

[0063]

[0064] Among them, ψ r_x is the residual magnetism of the x-phase converter transformer after opening, and u x(t) is the voltage curve of the phase x commutation transformer, where x is one of the phases A, B, and C. t1 is the lower limit of voltage integration; t2 is the upper limit of voltage integration. The upper limit of integration t2 should be as large as possible to ensure that the voltage decays to 0 at this time.

[0065] In step (3), determine the three-phase closing sequence according to the following method:

[0066] (a) Select the phase with the largest absolute value of residual magnetism as the first closing phase;

[0067] (b) Select the phase leading the first closing phase by 120° as the second closing phase.

[0068] In step (4), calculate the ideal no-load closing angle and the no-inrush current closing angle interval of the first closing phase according to the following method:

[0069] (a) Ensure that the transient component of the magnetic flux after the no-load closing of the first closing phase is 0, and then the ideal no-load closing angle can be obtained. Assume that the grid-side power supply of the first closing phase is u s =U m sinωt, then the ideal no-load closing angle of the first closing phase is:

[0070]

[0071] where θ fir_1 is the ideal no-load closing angle of the first closing phase, ψ r_fir is the residual magnetism after the disconnection of the commutation transformer of the first closing phase, and ψ m is the peak value of the magnetic flux during the rated operation of the commutation transformer.

[0072] (b) According to the closing resistor input time, calculate the closing angle θ a_fir at which the closing resistor has an inhibitory effect on the magnetizing inrush current and the closing angle θ b_fir that completely suppresses the magnetizing inrush current;

[0073]

[0074] where ψ dc_fir is the transient component of the magnetic flux after closing, and ψ s is the knee point of the magnetic flux.

[0075] (c) The no-inrush current closing angle interval of the first closing phase is [θ b_fir , θ fir_1 . Closing at any angle within the interval, no large-amplitude magnetizing inrush current will be generated in this phase.

[0076] In step (5), it is necessary to determine the closing angle of the first closing phase according to the dispersion of the breaker operation. In this embodiment, it is assumed that the dispersion of the advance and lag of each phase breaker is the same. Therefore, the midpoint of the inrush-free closing angle interval is selected as the closing angle of the first closing phase, that is:

[0077]

[0078] In step (6), the ideal no-load closing angle and the inrush-free closing angle interval of the second closing phase are calculated according to the following method:

[0079] (a) Ensure that the transient component of the magnetic flux after the no-load closing of the second closing phase is 0, and then the ideal no-load closing angle can be obtained. Since the initial phase α sec of the second closing phase is 120°, its ideal no-load closing angle is:

[0080]

[0081] Among them, ψ dc_sec is the transient component of the magnetic flux of the second closing phase after closing.

[0082] ψ dc_sec is calculated as follows:

[0083]

[0084] (b) According to the closing resistor input time, calculate the closing angle θ b_sec at which the closing resistor completely suppresses the magnetizing inrush current;

[0085]

[0086] (c) The inrush-free closing angle interval of the second closing phase is [θ b_sec , θ sec_1 . Closing the remaining two phases simultaneously at any angle within the interval will not generate a large-amplitude magnetizing inrush current for both phases.

[0087] In step (7), it is necessary to determine the closing angle of the second closing phase according to the dispersion of the breaker operation. In this embodiment, it is assumed that the dispersion of the advance and lag of each phase breaker is the same. Therefore, the midpoint of the inrush-free closing angle interval is selected as the closing angle of the second closing phase, and the remaining two phases are closed simultaneously after the first closing phase has been closed for one cycle.

[0088] To verify the inrush current suppression effect of the closing strategy proposed by the present invention under various working conditions, verification is carried out under various working conditions according to the method in the above embodiment.

[0089] Working condition 1: The residual magnetism is 0, and the closing resistor input times are 5 ms, 7 ms, 9 ms, and 11 ms respectively. Calculate the peak values of the magnetizing inrush current under different closing angles and closing resistor input times. The simulation results are asFigure 3 As shown in the figure, the calculation results of the closing angle interval are shown in Table 1.

[0090] Table 1 Calculation results of no-inrush closing angle interval under different closing resistor input times

[0091]

[0092] Condition 2: The closing resistor input time is 8 ms, and the residual magnetisms are -0.6 p.u., -0.3 p.u., 0 p.u., 0.3 p.u., and 0.6 p.u. respectively. The closing angle is parameter scanned to calculate the peak values of the exciting inrush current under different closing angles and residual magnetisms. The simulation results are as Figure 4 shown, and the calculation results of the closing angle interval are shown in Table 2.

[0093] Table 2 Calculation results of no-inrush closing angle interval under different residual magnetisms

[0094]

[0095]

[0096] It is verified that the proposed method for calculating the no-inrush closing angle interval can ensure that the no-load closing inrush current at any angle within the interval is less than 300 A under different residual magnetisms and closing angles.

[0097] At the same time, to ensure the effectiveness of the no-load closing strategy proposed based on the no-inrush closing angle interval, 72 equally spaced moments within one power frequency cycle are selected for opening to obtain different residual magnetism conditions, and the proposed no-load closing strategy is used for closing.

[0098] Condition 3: Assume that the closing resistor input time is 8 ms, the measurement of the residual magnetism is accurate, the breaker action has no deviation, and the inrush currents of each phase are as Figure 5 shown. In 72 groups of experiments, the peak values of the three-phase inrush currents are all less than 265.0 A, and the converter transformer can be put into operation normally. The results show that the method in this paper can suppress the exciting inrush current when there is residual magnetism.

[0099] Condition 4: Assume that the closing resistor input times are 8 ms and 11 ms. Biases not exceeding ±2 ms are added to the calculated closing angles of the first closing phase and the remaining closing phases by each method, and parametric scanning is performed with a step size of 0.5 ms, and closing is carried out under the aforementioned 72 residual magnetism conditions. A total of 5832 simulation experiments are carried out, and the results of the peak values of the exciting inrush current under different breaker action dispersions are as Figure 6 shown, and the characteristic values of the peak inrush current are shown in Table 3. The results show that the method proposed in this patent can achieve the suppression of the inrush current when the breaker action dispersion is large.

[0100] Table 3 Characteristics of the peak exciting inrush current when the breaker action has a deviation

[0101]

[0102] In summary, a method for formulating the no-load closing strategy of a conventional HVDC converter station based on the no-inrush closing angle interval proposed by the present invention can effectively suppress the exciting inrush current when the breaker action dispersion is large, and ensure the successful no-load commissioning of the converter transformer.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for formulating the no-load closing strategy of a converter station based on the inrush-free closing angle interval, characterized in that, The method specifically includes the following steps: S1: Obtain the voltage waveform when the three-phase converter transformer shuts down and the closing resistor input time; S2: Calculate and obtain the residual magnetism of the three-phase converter transformer according to the voltage waveform when the converter transformer shuts down; S3: Determine the closing sequence of the three phases according to the magnitude and direction of the residual magnetism of the three-phase converter transformer; S4: Determine the ideal no-load closing angle and the inrush-free closing angle interval of the first closing phase according to the residual magnetism of the first closing phase and the closing resistor input time; S5: Select the closing angle of the first closing phase within the inrush-free closing angle interval of the first closing phase according to the dispersion of the breaker operation, and ensure that the actual closing angle of the breaker is within the interval; S6: Determine the ideal no-load closing angle and the inrush-free closing angle interval of the second closing phase according to the selected closing angle of the first closing phase, the residual magnetism of the first closing phase and the closing resistor input time; S7: Select the closing angle of the second closing phase within the inrush-free closing angle interval of the second closing phase according to the dispersion of the breaker operation, and ensure that the actual closing angle of the breaker is within the interval.

2. The method for formulating the no-load closing strategy of a converter station according to claim 1, wherein In step S2, the calculation formula for the residual magnetism of the three-phase converter transformer is: where t1 is the lower limit of voltage integration, t2 is the upper limit of voltage integration, ψ r_x is the residual magnetism after the opening of the x-phase commutation transformer, and u x (t) is the voltage curve of the x-phase commutation transformer, and x is one of phase A, phase B, and phase C.

3. The method for formulating the no-load closing strategy of a converter station according to claim 1, wherein In step S3, the method for determining the three-phase closing sequence is divided into the following steps: S31: Select the phase with the largest absolute value of residual magnetism as the first closing phase; S32: Select the phase leading the first closing phase by 120° as the second closing phase.

4. The method for formulating the no-load closing strategy of a converter station according to claim 1, characterized in that, In step S4, the calculation formula for the ideal no-load closing angle of the first closing phase is: Among them, θ fir_1 is the ideal no-load closing angle of the first closing phase, ψ r_fir is the residual magnetism after the circuit breaker of the commutation transformer of the first closing phase is opened, ψ m is the peak value of the magnetic flux linkage during the rated operation of the commutation transformer.

5. The method for formulating the no-load closing strategy of the converter station according to claim 4, wherein In step S4, the inrush-free closing angle interval of the first closing phase is [θ b_fir , θ fir_1 , where θ b_fir is the closing angle at which the closing resistor of the first closing phase completely suppresses the magnetizing inrush current, and the expression is: where T is the closing resistor insertion time; ψ dc_fir is the transient component of the magnetic flux linkage of the first closing phase after closing, and the expression is: ψ dc_fir = -ψ m cosθ fir + ψ r_fir Among them, θ fir is the actual closing angle of the first closing phase.

6. The method for formulating the no-load closing strategy of a converter station according to claim 5, wherein Step S5 specifically includes: assuming that the action dispersions of the circuit breakers in each phase for advance and lag are the same, selecting the midpoint of the no-inrush closing angle interval as the actual closing angle of the first closing phase, that is:

7. The method for formulating the no-load closing strategy of a converter station according to claim 1, wherein In step S6, the calculation formula for the ideal no-load closing angle of the second closing phase is: Among them, θ sec_1 is the ideal no-load closing angle of the second closing phase, ψ dc_sec is the transient component of the flux linkage of the second closing phase after closing; ψ m is the peak value of the flux linkage during the rated operation of the converter transformer, α sec is the initial phase of the second closing phase.

8. The method for formulating the no-load closing strategy of the converter station according to claim 7, wherein, In step S6, the inrush-free closing angle interval of the second closing phase is [θ b_sec , θ sec_1 , where θ b_sec is the closing angle at which the closing resistor of the second closing phase completely suppresses the magnetizing inrush current; where T is the closing resistor insertion time; ψ dc_sec is the transient component of the magnetic flux linkage of the second closing phase after closing, and the expression is: Among them, θ fir is the actual closing angle of the first closing phase, and θ b_fir is the closing angle at which the closing resistor of the first closing phase completely suppresses the inrush current; ψ r_x is the residual magnetism after the circuit breaker of the converter transformer of phase x is opened, where x is one of phase A, phase B, and phase C; ψ s is the knee point of the magnetic flux; θ a_fir is the closing angle at which the closing resistor of the first closing phase has an inhibitory effect on the inrush current, and the expression is:

9. The method for formulating the no-load closing strategy of the converter station according to claim 8, characterized in that, Step S7 specifically includes: assuming that the action dispersions of the breakers of each phase in advance and lag are the same, select the midpoint of the inrush-free closing angle interval as the closing angle of the second closing phase, and close the remaining two phases simultaneously after the first closing phase has been closed for one cycle.

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