Variable speed pumped hydro additional power fluctuation suppression method, system and device

Abstract

A method for suppressing additional power fluctuations in variable-speed pumped-storage hydroelectric power generation is disclosed. This method first determines the low-pass filter time constant based on the State of Charge (SOC) value of the variable-speed pumped-storage hydroelectric power generation system when wind power fluctuation smoothing control is required. Then, wind power fluctuation smoothing control is performed based on the low-pass filter time constant. This invention not only has a good wind power fluctuation smoothing effect but also a fast smoothing speed.

Description

Technical Field

[0001] This invention belongs to the field of variable speed pumped storage control, specifically relating to a method, system, and equipment for suppressing additional power fluctuations in variable speed pumped storage. Background Technology

[0002] In the process of building a new power system, with the rapid development of new energy sources, efficient, mature, and safe energy storage technologies have become a key link. Compared with energy storage technologies such as electrochemical, compressed air, and flywheel, pumped hydro storage has advantages such as technological maturity, safe operation, and low carbon emissions. It also has the inherent characteristics of long regulation time and the ability to support system inertia, making it the most reliable and mature flexible regulation resource.

[0003] Currently, almost all pumped storage power stations in my country use reversible units with fixed speeds. Because the unit speed is not adjustable, the fixed speed, the unit's regulation function, and its operating range are all limited. Against this backdrop, variable-speed pumped storage power stations, which can achieve optimal efficiency in both turbine and pump operating conditions and flexibly adjust the active power absorbed under pump operating conditions, have begun to attract widespread attention both domestically and internationally.

[0004] Existing control strategies for variable-speed pumped storage to suppress power fluctuations suffer from unclear start-stop timings and mechanisms. For variable-speed pumped storage control that uses low-pass filtering to smooth power fluctuations, most methods rely on trial and error to obtain the low-pass filter time constant, lacking a reasonable mathematical derivation as a basis. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned problems in the prior art by providing a method, system, and equipment for suppressing additional power fluctuations in variable-speed pumped-storage hydroelectric power systems that offers fast and effective mitigation of wind power fluctuations.

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

[0007] A method for suppressing additional power fluctuations in variable-speed pumped storage includes:

[0008] When it is determined that wind power fluctuation smoothing control is required, the low-pass filter time constant is determined based on the SOC value of variable speed pumped storage.

[0009] Wind power fluctuation smoothing control based on low-pass filter time constant.

[0010] The process of determining the low-pass filter time constant based on the SOC value of variable-speed pumped storage includes:

[0011] S1. Calculate the low-pass filter time constant T according to the following formula:

[0012]

[0013] In the above formula, T min SOC is the minimum value of the low-pass filter time constant. vp The SOC value for variable speed pumped storage;

[0014] S2. Determine the final low-pass filter time constant T′ based on the following formula:

[0015]

[0016] In the above formula, T max This represents the maximum value of the low-pass filter time constant.

[0017] The minimum value T of the low-pass filter time constant min The following formula is used to calculate:

[0018]

[0019] In the above formula, k Pwind k Pwind_st These are the slope of the wind power output curve and its standard value;

[0020] The maximum value T of the low-pass filter time constant max The following formula is used to calculate:

[0021]

[0022] In the above formula, s is the minimum adjustable capacity on one side.

[0023] The minimum adjustable capacity s on one side is calculated using the following formula:

[0024]

[0025] In the above formula, P max P min These represent the maximum and minimum power that the variable-speed pumped storage hydroelectric power station can absorb or generate during its normal operating range, P. set P is the active power dispatch value for variable-speed pumped storage. up P down These refer to the active power that can be adjusted upwards and downwards in addition to the scheduled power of variable speed pumped storage.

[0026] The methods for determining the need for wind power fluctuation mitigation control include:

[0027] The slope of the wind power output curve is calculated based on wind power sampling data, and the slope of the wind power output curve is compared with the standard value of the slope. Based on the comparison results, it is determined whether wind power fluctuation smoothing control is needed.

[0028] The determination of whether wind power fluctuation smoothing control is needed based on the comparison results includes:

[0029] If the slope of the wind power output curve is greater than the standard slope value and the duration reaches t or more, then wind power fluctuation smoothing control is required; otherwise, wind power fluctuation smoothing control is not required.

[0030] The slope k of the wind power output curve Pwind The following formula is used to calculate:

[0031] k Pwind =(P t -P t-1 ) / Δt

[0032] In the above formula, P t P t-1 Δt represents the wind power at the current time and the previous sampling time, respectively, and Δt represents the duration between the current time and the previous sampling time.

[0033] The standard value of the slope k Pwind_st It is calculated based on the maximum change in active power of a wind farm over a certain period of time in the wind farm grid connection standard.

[0034] A variable-speed pumped storage additional power fluctuation suppression system includes a low-pass filter time constant calculation module and a low-pass filter module;

[0035] The low-pass filter time constant calculation module is used to determine the low-pass filter time constant based on the SOC value of variable speed pumped storage.

[0036] The low-pass filter module is used for wind power fluctuation smoothing control based on the low-pass filter time constant.

[0037] A variable-speed pumped storage additional power fluctuation suppression device includes a processor and a memory;

[0038] The memory is used to store computer program code and to transmit the computer program code to the processor;

[0039] The processor is used to execute the aforementioned variable-speed pumped storage additional power fluctuation suppression method according to the instructions in the computer program code.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] 1. The present invention provides a method for suppressing additional power fluctuations in variable-speed pumped storage. First, when it is determined that wind power fluctuation smoothing control is required, a low-pass filter time constant is determined based on the SOC value of the variable-speed pumped storage. Then, wind power fluctuation smoothing control is performed based on the low-pass filter time constant. On the one hand, this method makes full use of the capacity of variable-speed pumped storage beyond the active power dispatch value within the normal operating capacity range to suppress power fluctuations. This not only does not affect the dispatching and operation of variable-speed pumped storage, but also has a fast active power adjustment speed, a long adjustment time, a large adjustment capacity, and good economic efficiency. On the other hand, this method provides a reasonable calculation method for the low-pass filter constant, which can adaptively obtain the low-pass filter constant based on the SOC value of the variable-speed pumped storage. It does not require trial and error, has a fast calculation speed, and can ensure a good effect in smoothing wind power fluctuations.

[0042] 2. The present invention provides a method for suppressing additional power fluctuations in variable-speed pumped storage. This method determines whether wind power fluctuation suppression control is needed by comparing the slope of the wind power output curve with the standard slope value. When the slope of the wind power output curve is greater than the standard slope value and the duration reaches t or more, it is determined that wind power fluctuation suppression control is needed. This method uses the slope of the wind power output curve as the initiation criterion for wind power fluctuation suppression. It can start suppression before the wind power change exceeds the grid connection standard of the wind farm, which has the advantage of advance capability. The wind power change can be reduced instantly after the start of the suppression, and the effect is fast. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the process of the present invention.

[0044] Figure 2 This is a topology diagram of the IEEE 4M11B system with variable-speed pumped storage and wind farm used in Example 1.

[0045] Figure 3 This is a schematic diagram illustrating the calculation method for the time constant of a low-pass filter.

[0046] Figure 4 This is a schematic diagram illustrating the calculation method for the minimum adjustable capacity on one side.

[0047] Figure 5 This is a smoothness diagram of the wind power waveform under different low-pass filter time constants and single-sided adjustable minimum capacity.

[0048] Figure 6 The waveform and slope curve of wind power output of a wind farm in Guishan during a 24-hour period in 2020 are shown.

[0049] Figure 7 This graph shows the effect of wind power fluctuation mitigation control on the reduction of wind power variation during the 370-390 minute period under water pump operation.

[0050] Figure 8The original wind power output curve and the wind power output curve after low-pass filtering under different single-sided adjustable minimum capacity are shown.

[0051] Figure 9 The output curves of variable-speed pumped storage hydropower after low-pass filtering for different single-sided adjustable minimum capacities.

[0052] Figure 10 The speed curves of variable-speed pumped storage after low-pass filtering under different single-sided adjustable minimum capacity.

[0053] Figure 11 The SOC curves of variable-speed pumped storage after low-pass filtering for different single-sided adjustable minimum capacities.

[0054] Figure 12 This is a framework diagram of the system described in Example 2.

[0055] Figure 13 This is a frame diagram of the device described in Example 3. Detailed Implementation

[0056] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0057] Example 1:

[0058] like Figure 1 As shown, a method for suppressing additional power fluctuations in variable-speed pumped storage is described. Figure 2 The IEEE 4M11B system containing variable-speed pumped storage and wind farm (in the system, each of the four generators has a rated capacity of 900MW and a rated voltage of 20kV, the variable-speed pumped storage has a rated capacity of 100MW, node 1 is the balancing node, nodes 2, 3, and 4 are PV nodes, and nodes 5-11 are PQ nodes; under standard operating conditions, the active power outputs of generators 2, 3, and 4 are 700MW, 719MW, and 700MW respectively, and their node voltage amplitudes are 1.01, 1.03, and 1.01 respectively; the active power loads at nodes 7 and 9 are 967MW and 1767MW respectively, and the inductive reactive power loads are both 100Mvar; the capacitors connected in parallel at both ends of the line provide 200Mvar and 350Mvar of inductive reactive power to nodes 7 and 9 respectively) is used as the research object. The output waveform of a wind farm in Guishan during a 24-hour period in 2020 is used as the wind farm output (the wind farm has a rated capacity of 410MW, and the sampling time is 5min). The following steps are performed sequentially:

[0059] 1. In the "Wind Farm Grid Connection Standard" (GB / T 19963-2011), for wind farms with an installed capacity greater than 150MW, the maximum active power change over 10 minutes is specified as 50MW. Therefore, the standard value of the slope k is determined. Pwind_st=50MW / 10min=5MW / min.

[0060] 2. Calculate the slope k of the wind power output curve based on wind power sampling data. Pwind :

[0061] k Pwind =(P t -P t-1 ) / Δt

[0062] In the above formula, P t P t-1 Δt represents the wind power at the current time and the previous sampling time, respectively, and Δt represents the duration between the current time and the previous sampling time.

[0063] 3. Compare the slope of the wind power output curve with the standard slope value. If the slope of the wind power output curve is greater than the standard slope value of 5 MW / min and the duration is more than 1 minute, it is determined that wind power fluctuation smoothing control is required, and proceed to step 4. If the slope of the wind power output curve is greater than the standard slope value of 5 MW / min, but the duration is less than 1 minute, it is considered to be instantaneous noise and it is determined that wind power fluctuation smoothing control is not required. If the slope of the wind power output curve is less than or equal to the standard slope value of 5 MW / min, it is determined that the wind power fluctuation is within the normal range and wind power fluctuation smoothing control is not required.

[0064] 4. See Figure 3 The slope k of the wind power output curve Pwind Taking the point of exceeding the limit as the starting point, it is assumed that the output curve will continue with this slope for a certain period of time thereafter. When the original wind power output curve operates at this slope and generates wind power output of y per unit time, the wind power processed curve after low-pass filtering needs to undergo another low-pass filtering time constant T to reach y. Therefore, it is assumed that the time for the filtered curve to reach y is 1+T. To ensure that the fluctuation of the filtered wind power output meets the wind farm grid connection standards, it should be... This leads to the method for calculating the minimum value of the low-pass filter time constant:

[0065] |k Pwind_st |·(T+1)≥|k Pwind |

[0066] Right now therefore

[0067] Due to the characteristics of a low-pass filter, the time difference between the curve before and after filtering is T. Therefore, the maximum difference between the curves before and after filtering is... The adjustable capacity of variable-speed pumped storage is limited by the minimum adjustable capacity on one side; therefore, the low-pass filter time constant T should satisfy:

[0068]

[0069] Right now

[0070] For a unilaterally adjustable minimum capacity s, such as Figure 4 As shown, its definition is the minimum adjustable capacity on one side, which is the minimum capacity that the variable-speed pumped storage can adjust upwards or downwards outside of the dispatched output (input). We assume that in the stochastic scenario of wind power, the probability of wind power fluctuations generating start-up signals is the same whether they are upwards or downwards. Therefore, we take a smaller value so that the symmetrical value of the minimum adjustable capacity on one side with respect to active power dispatch is within the operating range, resulting in:

[0071]

[0072] In the above formula, P max P min These represent the maximum and minimum power that the variable-speed pumped storage hydroelectric power station can absorb or generate during its normal operating range, P. set P is the active power dispatch value for variable-speed pumped storage. up P down These refer to the active power that can be adjusted upwards and downwards in addition to the scheduled power of variable speed pumped storage.

[0073] This definition unifies the cases where the active power dispatch value is 0 and not 0 under the operating conditions of water pumps and turbines, and can systematically reflect the relationship between the size of adjustable capacity and smoothness.

[0074] 5. SOC value based on variable speed pumped storage vp Calculate the filter time constant T:

[0075]

[0076] 6. Determine the final low-pass filter time constant T′ based on the following formula:

[0077]

[0078] 7. The low-pass filter module performs wind power fluctuation smoothing control based on the final low-pass filter time constant, and continues for 2 hours, so that the period of severe wind power fluctuation is within the smoothing time range of the control strategy.

[0079] Under different pass filter time constants, variable-speed pumped storage with different single-sided adjustable minimum capacity s was used to smooth wind power fluctuations at a wind farm in Guishan. The effectiveness of the control strategy was verified by smoothness, and the results are as follows: Figure 5 As shown.

[0080] Figure 5The circles in the diagram represent the smoothness of the wind power waveform after using different single-sided adjustable minimum capacity s to smooth wind power fluctuations under different low-pass filtering time constants in variable-speed pumped storage. The smoothness r of the waveform is the ratio of the root variance between the first-order difference of the filtered signal and the first-order difference of the original signal. The smaller the value, the better the filtering effect. The specific calculation formula is as follows:

[0081]

[0082] In the above formula, f(n) is the original signal and f(n) is the filtered signal.

[0083] Curve fitting was performed on circles with the same low-pass filter time constant, resulting in three downward-sloping curves. The critical point represents the minimum adjustable capacity on one side that, under the three calculated low-pass filter constants, just barely meets the wind farm grid connection standards. Figure 5 It can be seen that the larger the value of 's', the more capacity variable-speed pumped storage can be used to smooth wind power fluctuations. Exceeding the critical value allows wind power to meet the grid connection standards of wind farms. When 's' is much smaller than the critical value, many smoothing actions are restricted, resulting in greater smoothness. When 's' is close to the critical value, most fluctuations can be smoothed. The inflection point of the curve represents the point of highest smoothing efficiency, indicating high capacity utilization of pumped storage, but it cannot completely smooth fluctuations. Therefore, the inflection point is located before the critical value. Increasing the capacity to the right of the critical point has little effect on improving smoothness.

[0084] The power output waveform of a wind farm in Guishan during a 24-hour period in 2020 was used as the wind farm output, with a sampling time of 5 minutes. Figure 6 The following figure shows the wind farm output waveform. The vertical axis represents the per-unit value based on the wind farm's rated capacity, and the horizontal axis represents time. The top figure shows the slope of this wind power output waveform, used to analyze the connection and disconnection times. The red dashed lines represent the connection and disconnection times; the first red dashed line represents the first connection, the second red dashed line represents the first disconnection, and so on. The last two times are represented by only one dashed line because the wind farm was immediately connected again after the penultimate disconnection. As can be seen from the figure, the period from 370min to 375min (marked by the red circle) is the period with the largest slope within 24 hours, and the period from 365min to 375min is the period with the largest change in wind power within 10 minutes. Therefore, this period is the focus of the analysis.

[0085] Simulations were conducted to verify the minimum adjustable capacity of 50MW and 25MW for a low-pass filter with a time constant T=1. Since the wind farm capacity is 410MW, according to the wind farm grid connection standard, a wind power variation exceeding 50MW is considered unqualified; therefore, the per-unit limit for wind power variation is 0.12. Starting from the 10th minute, the wind power output at each sampling point was subtracted from the wind power output 10 minutes prior to obtain the 10-minute wind power variation. The 10-minute wind power variation was plotted on the vertical axis, with time on the horizontal axis. Observing the vertical axis clearly shows whether the wind power variation exceeds the limit. The system was controlled to be activated at 270 minutes and deactivated at 390 minutes. The results show that the original wind power curve exceeded the limit most frequently during the period from 365 minutes to 375 minutes. Figure 6 Consistent. Since the wind power variation during the 10-minute period from 365 to 375 minutes is greater than 0.15, we take this moment as an example to observe whether wind power fluctuation smoothing control can make the smoothed waveform meet the wind farm grid connection standards. The effect of reducing wind power variation during the 370-390 minute period is shown in the graph below. Figure 7 As shown.

[0086] Depend on Figure 7 It can be seen that when T=1 and s=25, according to Figure 5 Since s has not yet reached the critical value, some fluctuations cannot be completely suppressed, resulting in a wind power change slightly greater than 0.12 after suppression, which does not meet the standard. When T=1 and s=50, s is exactly at the critical value, and the wind power change is less than 0.12, which can be suppressed to meet the standard. The above results demonstrate the effectiveness of this control strategy.

[0087] Finally, the impact of wind power fluctuation mitigation control on the operation of variable-speed pumped storage hydroelectric power generation under pump conditions was examined, and the results are as follows: Figure 8-11 As shown. Where s = 32.8 MW is the critical value for T = 0.67. (This is achieved through...) Figures 8-11 As can be seen, when s = 16.4MW, some waveforms are limited by the normal operating range of 0.6-1 pu for variable-speed pumped storage. The active power dispatch value of variable-speed pumped storage is 0.8 pu, and the regulation capacity within the ranges of 0.6-0.8 pu and 0.8-1 pu can be used for additional power fluctuation suppression. Due to the pumping operation, the power absorbed and the SOC value of variable-speed pumped storage continuously increase. However, due to the randomness of wind power fluctuations, power fluctuations outside the active power dispatch value of variable-speed pumped storage have little impact on the overall situation.

[0088] Example 2:

[0089] like Figure 12As shown, a variable-speed pumped storage additional power fluctuation suppression system includes a low-pass filter time constant calculation module 1 and a low-pass filter module 2. The low-pass filter time constant calculation module 1 is used to determine the low-pass filter time constant based on the SOC value of the variable-speed pumped storage; the low-pass filter module 2 is used to perform wind power fluctuation smoothing control based on the low-pass filter time constant.

[0090] Example 3:

[0091] like Figure 13 As shown, a variable-speed pumped-storage additional power fluctuation suppression device includes a processor 41 and a memory 42. The memory 42 is used to store computer program code 43 and transmit the computer program code 43 to the processor 41. The processor 41 is used to execute the variable-speed pumped-storage additional power fluctuation suppression method described in Embodiment 1 according to the instructions in the computer program code 43.

[0092] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0093] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0094] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0095] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0096] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0097] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for suppressing additional power fluctuations in variable-speed pumped-storage hydroelectric power, characterized in that, The method includes: When determining the need for wind power fluctuation mitigation control, the low-pass filter time constant is determined based on the SOC value of the variable-speed pumped storage system, including: S1. Calculate the low-pass filter time constant T according to the following formula: ； ； In the above formula, This represents the minimum value of the low-pass filter time constant. The SOC value for variable-speed pumped storage. , These are the slope of the wind power output curve and its standard value; S2. Determine the final low-pass filter time constant based on the following formula. : ； ； In the above formula, This represents the maximum value of the low-pass filter time constant. This is the minimum adjustable capacity on one side. Wind power fluctuation smoothing control based on low-pass filter time constant.

2. The method for suppressing additional power fluctuations in variable-speed pumped storage according to claim 1, characterized in that, The unilaterally adjustable minimum capacity The following formula is used to calculate: ； In the above formula, , These refer to the maximum and minimum power that the variable-speed pumped storage hydroelectric power station can absorb or generate during its normal operating range. This refers to the active power dispatch value for variable-speed pumped storage. , These refer to the active power that can be adjusted upwards and downwards in addition to the scheduled power of variable speed pumped storage.

3. The method for suppressing additional power fluctuations in variable-speed pumped storage according to claim 1, characterized in that, The methods for determining the need for wind power fluctuation mitigation control include: The slope of the wind power output curve is calculated based on wind power sampling data, and the slope of the wind power output curve is compared with the standard value of the slope. Based on the comparison results, it is determined whether wind power fluctuation smoothing control is needed.

4. The method for suppressing additional power fluctuations in variable-speed pumped storage according to claim 3, characterized in that, The determination of whether wind power fluctuation smoothing control is needed based on the comparison results includes: If the slope of the wind power output curve is greater than the standard slope value and the duration reaches t or more, then wind power fluctuation smoothing control is required; otherwise, wind power fluctuation smoothing control is not required.

5. The method for suppressing additional power fluctuations in variable-speed pumped storage according to claim 1, characterized in that, The slope of the wind power output curve The following formula is used to calculate: ； In the above formula, , These are the wind power at the current time and the previous sampling time, respectively. This represents the duration between the current time and the previous sampling time.

6. The method for suppressing additional power fluctuations in variable-speed pumped storage according to claim 1, characterized in that, The standard value of the slope It is calculated based on the maximum change in active power of a wind farm over a certain period of time in the wind farm grid connection standard.

7. A variable-speed pumped-storage hydroelectric power fluctuation suppression system, characterized in that, Includes low-pass filter time constant calculation module 1 and low-pass filter module 2; The low-pass filter time constant calculation module 1 is used to determine the low-pass filter time constant based on the SOC value of variable-speed pumped storage when it is determined that wind power fluctuation smoothing control is required, including: Calculate the low-pass filter time constant T using the following formula: ； ； In the above formula, This represents the minimum value of the low-pass filter time constant. The SOC value for variable-speed pumped storage. , These are the slope of the wind power output curve and its standard value; The final low-pass filter time constant is determined based on the following formula. : ； ； In the above formula, This represents the maximum value of the low-pass filter time constant. This is the minimum adjustable capacity on one side. The low-pass filter module 2 is used for wind power fluctuation smoothing control based on the low-pass filter time constant.

8. A variable-speed pumped-storage hydroelectric power fluctuation suppression device, characterized in that, Includes processor 41 and memory 42; The memory 42 is used to store computer program code 43 and transmit the computer program code 43 to the processor 41; The processor 41 is configured to execute the variable-speed pumped storage additional power fluctuation suppression method according to any one of claims 1-6, based on the instructions in the computer program code 43.

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