Three-stage new energy probabilistic annual power generation scene generation method

Abstract

The invention belongs to the technical field of power systems, and discloses a three-stage new energy probabilistic annual power generation scene generation method. The electric power and electric quantity characteristic indexes are calculated based on the new energy historical output data, the annual power generation scene is generated based on the characteristic indexes, and the original output characteristics of the new energy are effectively reserved. The method comprises the following steps: generating a probabilistic annual power generation utilization hour scene based on an adaptive clustering algorithm, taking a historical scene as a statistical basis, extracting probability characteristics of annual power generation utilization hours of the historical scene, and replacing the historical scene with a typical annual power generation utilization hour scene, thereby realizing probabilistic reduction of the historical output scene. And the system can carry out probabilistic operation simulation analysis conveniently. An original monthly electric quantity distribution curve and an hour-by-hour electric quantity distribution curve are matched by taking an annual power generation utilization hour number as an evaluation index, optimization adjustment is performed on the basis of a historical scene, and scene differences under different annual power generation utilization hour number levels are ensured while diversity of new energy output scenes is reserved.

Description

Technical Field

[0001] This invention relates to the technical field of power systems, and in particular to a three-stage probabilistic annual power generation scenario generation method for new energy sources. Background Technology

[0002] In recent years, due to the significant randomness and uncertainty of renewable energy output, its output characteristics over long timescales are difficult to accurately describe and characterize, making it challenging to generate renewable energy sequence scenarios on an annual timescale. Existing methods often construct typical daily scenario sequences and state transition matrices, determine the transitions of typical daily scenarios based on random sampling probabilities, and finally concatenate several typical daily scenario sequences to construct an annual scenario sequence. This method uses only a few typical daily scenarios as scenario generation samples, resulting in overly limited scenario types and failing to reflect the diversity of historical renewable energy daily output sequences. Furthermore, this lack of diversity leads to significant differences between the generated annual renewable energy output sequence scenarios and actual scenarios; it only guarantees consistency with historical scenarios in terms of probabilistic statistical characteristics and cannot reflect the actual changes in renewable energy output. Summary of the Invention

[0003] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by this invention is that the lack of diversity in existing technologies leads to significant differences between the generated annual output sequence of new energy sources and the actual scenario.

[0006] To address the aforementioned technical problems, this invention provides the following technical solution: a three-stage probabilistic annual power generation scenario generation method for new energy sources, comprising:

[0007] Acquire historical wind and solar power output data from the power system and perform per-unit processing;

[0008] After statistical processing, the annual power generation utilization hours of wind power and photovoltaic scenarios are used to obtain probabilistic annual power generation utilization hour scenarios by adaptively clustering the annual power generation utilization hours based on the annual power generation utilization hours, monthly power allocation curves, and hourly power allocation curves.

[0009] Based on the annual power generation utilization hours matched with the monthly power allocation curve, the annual power generation utilization hours are allocated to each month to obtain the probabilistic monthly power generation utilization hours scenario. Furthermore, based on the monthly power generation utilization hours matched with the hourly power allocation curve, the monthly power generation utilization hours are allocated to each hour within the month to obtain the probabilistic annual hourly power generation scenario.

[0010] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the per-unit processing method is expressed as follows:

[0011]

[0012]

[0013] in, P represents the per-unit value of wind power output. W P represents the actual output value of wind power. NW Indicates wind power installed capacity; P represents the per-unit value of photovoltaic power output. V P represents the actual output of photovoltaic power. NV This indicates photovoltaic installations.

[0014] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the utilization hours are expressed as:

[0015]

[0016]

[0017] Among them, T W,Y This indicates the annual utilization hours of wind power applications. T represents the per-unit value of wind power output at time t. V,Y This indicates the annual utilization hours of the photovoltaic scenario. This represents the per-unit value of photovoltaic power output at time t, and 8760 represents the wind and photovoltaic power output data obtained for 8760 points throughout the year.

[0018] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the monthly power allocation curve includes:

[0019] The monthly power generation utilization hours for historical wind and solar power scenarios are represented as follows:

[0020]

[0021]

[0022] Among them, T W,mT represents the monthly utilization hours of the wind power scenario in month m. V,m N represents the monthly utilization hours of the photovoltaic scenario in month m. m This represents the total number of moments in month m.

[0023] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the monthly power allocation curve is represented as follows:

[0024]

[0025] Among them, T m F represents the monthly power generation utilization hours in month m. m f represents the monthly power generation distribution in month m. a (m) represents the basic monthly electricity allocation curve.

[0026] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the monthly power allocation curve further includes:

[0027] By reducing the monthly electricity consumption in the dry season by 10% and increasing the monthly electricity consumption in the wet season by 10% in the basic monthly electricity distribution curve, we obtain the monthly electricity distribution curve f, which is characterized by low dry season and high wet season. b (m);

[0028] By increasing the monthly electricity consumption during the dry season by 10% and decreasing the monthly electricity consumption during the wet season by 10% in the basic monthly electricity consumption distribution curve, a monthly electricity consumption distribution curve f with high consumption during dry seasons and low consumption during wet seasons is obtained. c (m);

[0029] The probability of each of the three types of monthly electricity allocation curves is set to 1 / 3.

[0030] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the hourly power allocation curve includes:

[0031]

[0032] in, F represents the per-unit value of power generation output at time t in month m. m,h Let f(m,t) represent the distribution of power generation at time t in month m, and let f(m,t) represent the hourly power distribution curve for month m.

[0033] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the probabilistic annual power generation utilization hours scenario includes:

[0034] Using historical annual power generation utilization hours as clustering samples, the DBSCAN clustering algorithm is used to perform adaptive clustering of annual power generation utilization hours, resulting in N clusters. Y Each annual power generation utilization hour scenario and its corresponding scenario probability p Y .

[0035] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the probabilistic monthly power generation utilization hours scenario includes:

[0036] For N Y For each annual power generation utilization hour scenario, a monthly power allocation curve is matched based on the annual power generation utilization hours. The monthly power allocation curve of the historical scenario with the closest annual power generation utilization hours is selected, including the basic monthly power allocation curve f. a (m), Monthly electricity distribution curve with low rainfall and high yields f b (m), Monthly electricity distribution curve with high peak and low off-peak periods (f) c (m);

[0037] Based on the monthly power allocation curve, the annual power generation utilization hours are allocated to each month, resulting in three allocation outcomes. This means there are three probabilistic scenarios for monthly power generation utilization hours each month, with each scenario having a probability of 1 / 3*p. Y .

[0038] As a preferred embodiment of the three-stage probabilistic annual power generation scenario generation method for new energy described in this invention, the probabilistic annual hourly power generation scenario includes:

[0039] For the probabilistic monthly power generation utilization hours scenario, the hourly power allocation curve is matched based on the monthly power generation utilization hours, and the hourly power allocation curve of the corresponding month with the closest monthly power generation utilization hours is selected.

[0040] Based on the hourly power allocation curve, the monthly power generation utilization hours are allocated to each hour to obtain the probabilistic hourly power generation scenario.

[0041] The beneficial effects of this invention are as follows: This invention provides a three-stage probabilistic annual power generation scenario generation method for new energy sources. Based on historical new energy output data, it calculates power characteristic indicators and generates annual power generation scenarios based on these indicators, effectively preserving the original output characteristics of new energy sources. It generates probabilistic annual power generation utilization hours scenarios based on an adaptive clustering algorithm. Using historical scenarios as a statistical basis, it extracts the probabilistic characteristics of annual power generation utilization hours from historical scenarios and replaces historical scenarios with typical annual power generation utilization hours scenarios, achieving a probabilistic reduction of historical output scenarios and facilitating probabilistic operation simulation analysis of the system. Using annual power generation utilization hours as an evaluation indicator, it matches the original monthly power allocation curve and hourly power allocation curve, optimizing and adjusting based on historical scenarios. This preserves the diversity of new energy output scenarios while ensuring the differences in scenarios under different annual power generation utilization hour levels. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0043] Figure 1 This is an overall flowchart of the three-stage probabilistic annual power generation scenario generation method for new energy sources according to an embodiment of the present invention;

[0044] Figure 2 This is a historical wind power scenario utilization hour distribution curve of the three-stage probabilistic annual power generation scenario generation method for new energy described in an embodiment of the present invention;

[0045] Figure 3 This is a historical photovoltaic scenario utilization hours distribution curve of the three-stage probabilistic annual power generation scenario generation method for new energy described in an embodiment of the present invention;

[0046] Figure 4 This is a diagram showing the monthly utilization hours allocation result of wind power scenario 1 in the three-stage probabilistic annual power generation scenario generation method of new energy described in an embodiment of the present invention.

[0047] Figure 5 This is a diagram showing the monthly utilization hours allocation result of photovoltaic scenario 1 in the three-stage probabilistic annual power generation scenario generation method of new energy described in an embodiment of the present invention. Detailed Implementation

[0048] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0049] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0050] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0051] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0052] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0053] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0054] Example 1

[0055] Reference Figure 1As one embodiment of the present invention, this embodiment provides a three-stage probabilistic annual power generation scenario generation method for new energy sources, including:

[0056] S1: Obtain historical wind power and photovoltaic power output data of the power system and perform per-unit processing;

[0057] Furthermore, the per-unit processing method is expressed as follows:

[0058]

[0059]

[0060] in, P represents the per-unit value of wind power output. W P represents the actual output value of wind power. NW Indicates wind power installed capacity; P represents the per-unit value of photovoltaic power output. V P represents the actual output of photovoltaic power. NV This indicates photovoltaic installations.

[0061] S2: After statistical processing, the annual power generation utilization hours, monthly power distribution curve, and hourly power distribution curve of wind power and photovoltaic scenarios are used to adaptively cluster the annual power generation utilization hours to obtain the probabilistic annual power generation utilization hours scenario.

[0062] Furthermore, the usage hours are expressed as:

[0063]

[0064]

[0065] Among them, T W,Y This indicates the annual utilization hours of wind power applications. T represents the per-unit value of wind power output at time t. V,Y This indicates the annual utilization hours of the photovoltaic scenario. This represents the per-unit value of photovoltaic power output at time t, and 8760 represents the wind and photovoltaic power output data obtained for 8760 points throughout the year.

[0066] It should be noted that there are 365 days in a year, and 24 moments in a day. 365 * 24 = 8760, so 8760 means that the curve is an annual curve, and the whole hour is taken.

[0067] Furthermore, the monthly electricity allocation curve includes:

[0068] The monthly power generation utilization hours for historical wind and solar power scenarios are represented as follows:

[0069]

[0070]

[0071] Among them, T W,m T represents the monthly utilization hours of the wind power scenario in month m. V,m N represents the monthly utilization hours of the photovoltaic scenario in month m. m This represents the total number of moments in month m.

[0072] The monthly electricity allocation curve is shown as follows:

[0073]

[0074] Among them, T m F represents the monthly power generation utilization hours in month m. m f represents the monthly power generation distribution in month m. a (m) represents the basic monthly electricity allocation curve.

[0075] Furthermore, the monthly electricity allocation curve also includes:

[0076] By reducing the monthly electricity consumption in the dry season by 10% and increasing the monthly electricity consumption in the wet season by 10% in the basic monthly electricity distribution curve, we obtain the monthly electricity distribution curve f, which is characterized by low dry season and high wet season. b (m);

[0077] By increasing the monthly electricity consumption during the dry season by 10% and decreasing the monthly electricity consumption during the wet season by 10% in the basic monthly electricity consumption distribution curve, a monthly electricity consumption distribution curve f with high consumption during dry seasons and low consumption during wet seasons is obtained. c (m);

[0078] The probability of each of the three types of monthly electricity allocation curves is set to 1 / 3.

[0079] Furthermore, the hourly power distribution curve includes:

[0080]

[0081] in, F represents the per-unit value of power generation output at time t in month m. m,h Let f(m,t) represent the distribution of power generation at time t in month m, and let f(m,t) represent the hourly power distribution curve for month m.

[0082] S3: Based on the annual power generation utilization hours, match the monthly power allocation curve, allocate the annual power generation utilization hours to each month to obtain the probabilistic monthly power generation utilization hours scenario, and based on the monthly power generation utilization hours, match the hourly power allocation curve to allocate the monthly power generation utilization hours to each hour within the month to obtain the probabilistic annual hourly power generation scenario.

[0083] Furthermore, in the probabilistic annual power generation utilization hours scenario, this involves using historical annual power generation utilization hours as clustering samples and employing the DBSCAN clustering algorithm to adaptively cluster annual power generation utilization hours, resulting in N clusters. Y Each annual power generation utilization hour scenario and its corresponding scenario probability p Y .

[0084] Furthermore, scenarios involving probabilistic monthly power generation utilization hours include:

[0085] For N Y For each annual power generation utilization hour scenario, a monthly power allocation curve is matched based on the annual power generation utilization hours. The monthly power allocation curve of the historical scenario with the closest annual power generation utilization hours is selected, including the basic monthly power allocation curve f. a (m), Monthly electricity distribution curve with low rainfall and high yields f b (m), Monthly electricity distribution curve with high peak and low off-peak periods (f) c (m);

[0086] Based on the monthly power allocation curve, the annual power generation utilization hours are allocated to each month, resulting in three allocation outcomes. This means there are three probabilistic scenarios for monthly power generation utilization hours each month, with each scenario having a probability of 1 / 3*p. Y .

[0087] Furthermore, probabilistic hourly power generation scenarios include:

[0088] For the probabilistic monthly power generation utilization hours scenario, the hourly power allocation curve is matched based on the monthly power generation utilization hours, and the hourly power allocation curve of the corresponding month with the closest monthly power generation utilization hours is selected.

[0089] Based on the hourly power allocation curve, the monthly power generation utilization hours are allocated to each hour to obtain the probabilistic hourly power generation scenario.

[0090] Example 2

[0091] Reference Figure 2 —5 is an embodiment of the present invention, which provides a three-stage probabilistic annual power generation scenario generation method for new energy sources. In order to prove the beneficial effects of the present invention, specific experimental data are used for scientific demonstration.

[0092] This example is based on historical wind power and photovoltaic power output data from a southern province from 2018 to 2021. The data type is curve data of 365×24 points.

[0093] (1) Statistical analysis of historical wind power and photovoltaic scenarios, including annual power generation utilization hours, monthly power distribution curves, and hourly power distribution curves, etc. Some data are shown in Tables 1-2. Figure 2 —As shown in Figure 3.

[0094] Table 1. Historical Wind Power Utilization Hours Statistics (Unit: h)

[0095]

[0096] Table 2. Historical Utilization Hours of Photovoltaic Scenarios (Unit: h)

[0097]

[0098]

[0099] (2) Adaptive clustering of annual power generation utilization hours was performed to obtain probabilistic annual power generation utilization hours scenarios, and the results are shown in Table 3-4.

[0100] Table 3. Scenarios of Probabilistic Annual Utilization Hours for Wind Power

[0101]

[0102] Table 4. Scenarios of Probabilistic Annual Utilization Hours for Photovoltaics

[0103]

[0104] (3) Based on the annual power generation utilization hours matched with the monthly power allocation curve, the annual power generation utilization hours are allocated to each month to obtain the probabilistic monthly power generation utilization hours scenario. The monthly power allocation results of wind power annual utilization hours scenario 1 and photovoltaic annual utilization hours scenario 1 are shown in Tables 5-6. Figure 4 As shown in Figure 5.

[0105] Table 5. Monthly Utilization Hours Allocation Results for Wind Power Scenario 1 (Unit: h)

[0106]

[0107] Table 6. Monthly Utilization Hours Allocation Results for Photovoltaic Scenario 1 (Unit: h)

[0108]

[0109] (4) Based on the monthly power generation utilization hours, match the hourly power allocation curve and allocate the monthly power generation utilization hours to the hourly within the month to obtain the probabilistic annual hourly power generation scenario.

[0110] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A three-stage probabilistic annual power generation scenario generation method for new energy sources, characterized in that, include: Acquire historical wind and solar power output data from the power system and perform per-unit processing; After statistical processing, the annual power generation utilization hours of wind power and photovoltaic scenarios are used to obtain probabilistic annual power generation utilization hour scenarios by adaptively clustering the annual power generation utilization hours based on the annual power generation utilization hours, monthly power allocation curves, and hourly power allocation curves. Based on the annual power generation utilization hours matched with the monthly power allocation curve, the annual power generation utilization hours are allocated to each month to obtain the probabilistic monthly power generation utilization hours scenario. Furthermore, based on the monthly power generation utilization hours matched with the hourly power allocation curve, the monthly power generation utilization hours are allocated to each hour within the month to obtain the probabilistic annual hourly power generation scenario.

2. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 1, characterized in that: The per-unit processing method is expressed as follows: in, P represents the per-unit value of wind power output. W P represents the actual output value of wind power. NW Indicates wind power installed capacity; P represents the per-unit value of photovoltaic power output. V P represents the actual output of photovoltaic power. NV This indicates photovoltaic installations.

3. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 2, characterized in that: The number of utilization hours is expressed as: Among them, T W,Y This indicates the annual utilization hours of wind power applications. T represents the per-unit value of wind power output at time t. V,Y This indicates the annual utilization hours of the photovoltaic scenario. This represents the per-unit value of photovoltaic power output at time t, and 8760 represents the wind and photovoltaic power output data obtained for 8760 points throughout the year.

4. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 3, characterized in that: The monthly electricity allocation curve includes: The monthly power generation utilization hours for historical wind and solar power scenarios are represented as follows: Among them, T W,m T represents the monthly utilization hours of the wind power scenario in month m. V,m N represents the monthly utilization hours of the photovoltaic scenario in month m. m This represents the total number of moments in month m.

5. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 4, characterized in that: The monthly electricity allocation curve is represented as follows: Among them, T m F represents the monthly power generation utilization hours in month m. m f represents the monthly power generation distribution in month m. a (m) represents the basic monthly electricity allocation curve.

6. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 5, characterized in that: The monthly electricity allocation curve also includes: By reducing the monthly electricity consumption in the dry season by 10% and increasing the monthly electricity consumption in the wet season by 10% in the basic monthly electricity distribution curve, we obtain the monthly electricity distribution curve f, which is characterized by low dry season and high wet season. b (m); By increasing the monthly electricity consumption during the dry season by 10% and decreasing the monthly electricity consumption during the wet season by 10% in the basic monthly electricity consumption distribution curve, a monthly electricity consumption distribution curve f with high consumption during dry seasons and low consumption during wet seasons is obtained. c (m); The probability of each of the three types of monthly electricity allocation curves is set to 1 / 3.

7. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 6, characterized in that: The hourly power distribution curve includes: in, F represents the per-unit value of power generation output at time t in month m. m,h Let f(m,t) represent the distribution of power generation at time t in month m, and let f(m,t) represent the hourly power distribution curve for month m.

8. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 7, characterized in that: The probabilistic annual power generation utilization hours scenario includes: Using historical annual power generation utilization hours as clustering samples, the DBSCAN clustering algorithm is used to perform adaptive clustering of annual power generation utilization hours, resulting in N clusters. Y Each annual power generation utilization hour scenario and its corresponding scenario probability p Y .

9. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 8, characterized in that: The probabilistic monthly power generation utilization hours scenario includes: For N Y For each annual power generation utilization hour scenario, a monthly power allocation curve is matched based on the annual power generation utilization hours. The monthly power allocation curve of the historical scenario with the closest annual power generation utilization hours is selected, including the basic monthly power allocation curve f. a (m), Monthly electricity distribution curve with low rainfall and high yields f b (m), Monthly electricity distribution curve with high peak and low off-peak periods (f) c (m); Based on the monthly power allocation curve, the annual power generation utilization hours are allocated to each month, resulting in three allocation outcomes. This means there are three probabilistic scenarios for monthly power generation utilization hours each month, with each scenario having a probability of 1 / 3*p. Y .

10. The three-stage probabilistic annual power generation scenario generation method for new energy sources as described in claim 9, characterized in that: The probabilistic annual hourly power generation scenario includes: For the probabilistic monthly power generation utilization hours scenario, the hourly power allocation curve is matched based on the monthly power generation utilization hours, and the hourly power allocation curve of the corresponding month with the closest monthly power generation utilization hours is selected. Based on the hourly power allocation curve, the monthly power generation utilization hours are allocated to each hour to obtain the probabilistic hourly power generation scenario.

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