An improved Jensen-Lissaman wake model suitable for complex mountainous terrain

Abstract

The present invention relates to the field of wind power generation technology, and discloses a wake model suitable for complex mountainous areas, comprising the following steps: Step 1, obtaining wind turbine parameters, thrust coefficient C T , hub height h, altitude Z; step 2, calculate the wind speed change caused by the change in altitude according to the Lissaman wake model; step 3, calculate the improved wake shielding based on the mountain terrain wind effect according to the Jensen wake model; the purpose of the present invention is to improve the prediction accuracy of the flow field in the wind turbine wake area, increase the power generation of the wind farm, and provide important technical support for the wake control of the wind farm, and propose an improved method for calculating the wind turbine wake by combining the Jensen wake model and the Lissaman wake model taking into account the terrain wind effect.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power generation, and in particular to an improved Jensen-Lissaman wake model suitable for complex mountainous areas. Background Art

[0002] The wake effect of wind turbines is one of the main factors affecting the overall power generation of wind farms. Accurately assessing the velocity distribution in the wake zone can optimize the layout of wind turbines within a wind farm, increasing the farm's power generation. It also provides important technical support for wind farm wake control. Most of my country's inland areas are mountainous and hilly, with mountainous terrain accounting for approximately 70% of the country's land area. Compared with flat terrain, wind farms in complex terrain (such as mountainous areas) often have better wind energy resources and broader development space, and are also a key area of ​​development for wind power in my country. Therefore, there is an urgent need to propose a wake model suitable for mountainous conditions.

[0003] Currently, analytical wake models are the most commonly used wake assessment models due to their simple principles and fast computational speed. Researchers have proposed various analytical wake models, of which the Jensen wake model is the most widely used. However, because it fails to consider the impact of altitude changes on wakes between wind turbines, this model's wake predictions are only applicable to flat terrain and suffer from limited accuracy. The Lissaman wake model calculates the effects of wakes between wind turbines at different altitudes, so combining these two wake models is a suitable approach. However, in addition to wind speed, wind direction is also a key factor in calculating wind turbine wakes, and the "orographic wind effect" is one of the most important factors influencing wind direction variations. The "orographic wind effect" refers to the phenomenon in which wind flow characteristics change due to the undulations and variations of the terrain. On a hillside, wind flow rises or falls along the slope, causing vertical changes in wind direction. Failure to account for wind direction changes caused by the "orographic wind effect" can lead to significant errors in wake predictions. Therefore, developing a wake model that considers the "orographic wind effect" is crucial for mountainous terrain. Summary of the Invention

[0004] The present invention aims to improve the prediction accuracy of the flow field in the wind turbine wake area, increase the power generation of wind farms, and provide important technical support for the control of wind farm wakes. An improved method for calculating wind turbine wakes that considers the "terrain wind effect" and combines the Jensen wake model with the Lissaman wake model is proposed. The method includes the following steps:

[0005] A wake model suitable for complex mountainous terrain includes the following steps:

[0006] Step 1: Obtain wind turbine parameters, thrust coefficient CT , hub height h, impeller radius r, altitude Z of each wind turbine, and determine the coordinate parameters of each wind turbine;

[0007] Step 2: Calculate the wind speed change caused by altitude change based on the Lissaman wake model;

[0008] Step 3: Calculate the wake turbulence obstruction according to the Jensen wake model.

[0009] Furthermore, the step 2 is specifically as follows:

[0010] Step 2-1: Based on the Lissaman wake model, assume that the wind speed changes exponentially with height. In the absence of a wake, the upstream wind turbine is i and the downstream wind turbine is j.

[0011] The wind speed of wind turbine i is:

[0012]

[0013] The wind speed of wind turbine j is:

[0014]

[0015] In the formula is the wind shear index; v0 is the incident wind speed, z0 is the incident wind altitude, z i is the altitude of the i-th wind turbine, z j is the altitude of the j-th wind turbine, h is the hub height of the wind turbine;

[0016] Step 2-2: When affected by the wake, assume that the wind speed reduction coefficient of wind turbine i is d i , the wind speed reduction coefficient of wind turbine j is d j ; The actual wind speed of wind turbine i and wind turbine j is:

[0017] v′ i =v i (1-d i ) (3)

[0018] v′ j =v j (1-d j ) (4)

[0019] Furthermore, the step 3 is specifically as follows:

[0020] Step 3-1, when i is the upstream wind turbine and j is the downstream wind turbine;

[0021] The influence of the wake of wind turbine i on wind turbine j is expressed as:

[0022] dj =β ij ×d ij (5)

[0023] Where: β ij is the weight of the intersection area between the wind turbine and the wake; d ij is the wake loss when wind turbine j is completely blocked by the wake of turbine i;

[0024] β ij =A ij / (πr 2 ) (6)

[0025] Where: A ij is the intersection area of ​​the wind turbine j and the wake area at position i, and r is the radius of the wind rotor;

[0026] According to the Jensen wake model, under full shielding conditions, the wake loss of wind turbine j is:

[0027] When the fans have the same height:

[0028]

[0029] When the fan height is different:

[0030]

[0031] Where: Cr is the thrust coefficient of the wind turbine; k is the wake diffusion coefficient; X is the distance between the two wind turbines in the wind direction; h is the wheel height; ΔZ is the height difference between the two wind turbines |Z i -Z j |;

[0032] In a wind farm, each wind turbine will be affected by the wake of multiple wind turbines to varying degrees under different wind direction conditions. Assuming that kinetic energy loss and wake loss are conserved, the wake effect on the j-th wind turbine can be calculated using the following formula:

[0033]

[0034] Where v ij is the speed of wind turbine j when it is completely blocked by the wake of turbine i;

[0035] Step 3-2, when j is the upstream wind turbine and i is the downstream wind turbine;

[0036] The influence of the wake of wind turbine i on wind turbine i is:

[0037] d i =β ji ×d ji (10)

[0038] Where:

[0039] β ji =A ji / (πr 2 ) (11)

[0040] d ji is the wake loss suffered by wind turbine i when it is completely blocked by the wake of wind turbine j;

[0041] When the fans have the same height:

[0042]

[0043] When the fan height is different:

[0044]

[0045] In an actual wind farm, each wind turbine will be affected by the wake of multiple wind turbines to varying degrees under different wind direction conditions. Assuming that kinetic energy loss and wake loss are conserved, the wake effect on the i-th wind turbine is calculated using the following formula:

[0046]

[0047] Where v ji is the speed when wind turbine i is completely blocked by the wake of wind turbine j.

[0048] Further, Usually 1 / 7 is taken, and it can also be calculated based on wind measurement data at different heights. The formula is as follows:

[0049]

[0050] Among them, v1 is the wind speed at height z1, and v2 is the wind speed at height z2.

[0051] Furthermore, in step 3:

[0052] In mountainous conditions, the incident wind will be affected by the "topographic wind effect". Under the influence of the hillside, the wind flow will be affected by the upward effect and the angle will change in the vertical direction. The angle between the vertical and horizontal wind direction is θ. Therefore, the calculation of the intersection area of ​​the wake area is shown as follows

[0053]

[0054] Where: is the radius of the circle after the wake diffusion, b is the wake diffusion coefficient;

[0055]

[0056] The beneficial effects of the present invention are as follows:

[0057] This invention takes into account the fact that incident wind in mountainous wind farms is affected by the "topographic wind effect." This effect, caused by the hillside, causes the wind flow to rise, resulting in a vertical angle change in wind direction. Therefore, when calculating the wake shielding area, the effect of varying wind direction angles on the wake shielding area must be considered. By accounting for this effect, the invention improves the accuracy of wake calculations, which is of great significance for wind farm microsite selection and power generation forecasting. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic flow diagram of the present invention;

[0059] Figure 2 is the Lissaman wake model;

[0060] Figure 3 This is a schematic diagram of Jensen wake model occlusion;

[0061] Figure 4 It is the obstruction profile of Jensen wake model;

[0062] Figure 5 is the intersection area between wind turbine j and the wake region at position i;

[0063] Figure 6 It is a schematic diagram of the coordinate axis and fan position. DETAILED DESCRIPTION

[0064] The wake model proposed in the present invention is described in detail below with reference to the accompanying drawings.

[0065] Step 1: Obtain wind turbine parameters, thrust coefficient C T , hub height h, rotor radius r, altitude Z, and with the dominant wind direction as the X-axis, determine the coordinate parameters of each wind turbine, such as Figure 6 shown.

[0066] Step 2: Calculate the wind speed change caused by altitude change based on the Lissaman wake model, such as Figure 2 Shown is the Lissaman wake model.

[0067] According to the Lissaman wake model, assuming that the wind speed changes exponentially with height, in the absence of a wake:

[0068] The wind speed of wind turbine i is

[0069]

[0070] The wind speed of wind turbine j is

[0071]

[0072] In the formula is the wind shear index, usually taken as 1 / 7. It can also be calculated based on wind data at different heights.

[0073]

[0074] When affected by the wake, it is assumed that the wind speed reduction coefficient of wind turbine i is d i , the wind speed reduction coefficient of wind turbine j is d j ; The actual wind speed of wind turbine i and wind turbine j is

[0075]

[0076] Step 3: Calculate the wake shielding according to the Jensen wake model, as follows: Figure 2 and Figure 3 As shown. Figure 2 Stroke direction from left to right

[0077] i is the upstream wind turbine, and j is the downstream wind turbine. Assume a "conical" wake region. The shape of the cone is related to the wake diffusion coefficient k. When the turbine rotor of turbine j intersects this wake region, turbine j will be affected by the wake. The larger the intersection area, the greater the impact.

[0078] Jensen wake and its impact on downstream wind turbines Figure 3 and Figure 4 As shown, the large circle represents the downstream wake area, and the small circle represents the rotor of the downstream wind turbine. Cases A, B, and C represent partial, full, and no obstruction, respectively. When fully obstructed, the wind turbine is most affected by the wake. When partially obstructed, the wind turbine's wake is affected proportionally to the obstruction area. When fully obstructed, the wind turbine is unaffected by the wake. Wind turbine i is the upstream wind turbine and is unaffected by the wakes of other wind turbines.

[0079] d i =0 (26)

[0080] The influence of the wake of wind turbine j on wind turbine i can be expressed as:

[0081] d j =β ij ×d ij (27)

[0082] Where: β ij is the weight of the intersection area between the wind turbine and the wake; d ij is the wake loss coefficient when wind turbine j is completely blocked by the wake of turbine i.

[0083] βij =A ij / (πr 2 ) (28)

[0084] Where: r is the radius of the wind wheel, A ij is the intersection area between wind turbine j and the wake area at position i, such as Figure 5 shown.

[0085] However, in mountainous conditions, the incident wind will be affected by the "orographic wind effect", and the wind flow will be affected by the upward force of the hillside, and the angle will change in the vertical direction. Figure 6 As shown, the angle between the vertical and horizontal wind directions. Therefore, the calculation of the intersection area of ​​the wake region is as follows:

[0086]

[0087] For the acquisition of angle θ, this application uses numerical simulation to derive a general rule. θ is determined according to different incident wind speeds, surface roughness, and slopes.

[0088] Where: is the radius of the circle after the wake diffusion, and the wake diffusion coefficient b = 0.08

[0089]

[0090] According to Jensen wake model, under full occlusion conditions, Figure 2 The wake loss of j in (a) is

[0091]

[0092] Figure 2 The wake loss of fan j in (b) is

[0093]

[0094] Where: Cr is the thrust coefficient of the wind turbine; k is the wake diffusion coefficient; X is the distance between the two wind turbines projected in the wind direction; h is the wheel height; ΔZ is the height difference between the two wind turbines |z i -z j |. Step 3-2, when Figure 2 The stroke direction is from right to left.

[0095] j is the upstream wind turbine, i is the downstream wind turbine, and wind turbine j will not be affected by the wake.

[0096] d j =0 (36)

[0097] The effect of the wake on wind turbine i is

[0098] d i =β ji ×d ji (37)

[0099] Where:

[0100] β ji =A ji / (πr 2 ) (38)

[0101] d ji is the wake loss suffered by wind turbine i when it is completely blocked by the wake of wind turbine j.

[0102] Figure 2 The wake loss of wind turbine i in (a) is

[0103]

[0104] Figure 2 The wake loss of wind turbine i in (b) is

[0105]

[0106] In an actual wind farm, each wind turbine will be affected by the wake of multiple wind turbines to varying degrees under different wind direction conditions. Assuming that kinetic energy loss and wake loss are conserved, the wake effect on the i-th wind turbine is calculated using the following formula:

[0107]

[0108] Where v ji is the speed when wind turbine i is completely blocked by the wake of wind turbine j.

[0109] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, which are intended to explain the present invention rather than to limit it.

[0110] Parameters of this embodiment: incident wind speed v0 = 7.49 m / s, Z0 = 1910 m, wind shear index Wake diffusion coefficient b = 0.08

[0111] The selected wind turbine parameters are: hub height h = 105m, rotor radius r = 86m, and the wind turbine thrust coefficient C at the incident wind speed T =0.541, the dominant wind direction is the X axis;

[0112] The first wind turbine has an altitude of Z1 = 1805, the second wind turbine has an altitude of Z2 = 1868, and the distance between the two wind turbines in the X-axis direction is ΔX = 296m;

[0113] First, calculate the wind speed of the second wind turbine under unobstructed conditions. According to the Lissaman wake model, the wind speed changes exponentially with height.

[0114]

[0115] Next, calculate the weight of the intersection area of ​​the wake region

[0116] Calculate the radius of the wake after diffusion

[0117]

[0118] Through numerical simulation methods, based on the actual terrain, the wind direction at the location of the second wind turbine is simulated:

[0119] V X =9.76m / s, V y =4.11m / s, V z =2.92m / s

[0120] Therefore, we can get

[0121] tanθ=0.299

[0122] Calculate the wake intersection area

[0123]

[0124] Calculate the area weight of the wake intersection area

[0125] β ij =A ij / (πr 2 )=0.774 (45)

[0126] Calculate the wake loss coefficient under complete wake obstruction

[0127]

[0128] Calculate the wake loss coefficient under actual obstruction conditions

[0129] d j =β ij ×d ij =0.134 (47)

[0130] Calculate final wind speed

[0131] v′ j =v j (1-d j )=6.51m / s (48).

Claims

1. A wake model suitable for complex mountainous terrain, characterized in that: The steps include: Step 1: Obtain wind turbine parameters, thrust coefficient C T , hub height h, impeller radius r, altitude Z of each wind turbine, and determine the coordinate parameters of each wind turbine; Step 2: Calculate the wind speed change caused by altitude change based on the Lissaman wake model; Step 3: Calculate the wake turbulence obstruction according to the Jensen wake model; Step 3-1, when i is the upstream wind turbine and j is the downstream wind turbine; The influence of the wake of wind turbine i on wind turbine j is expressed as: d j =b ij ×d ij (1) Where: β ij is the weight of the intersection area between the wind turbine and the wake; d ij is the wake loss coefficient when wind turbine j is completely blocked by the wake of turbine i; β ij ＝A ij / (πr 2 ) (2) Where: A ij is the intersection area of ​​the wind turbine j and the wake area at position i, and r is the radius of the wind rotor; According to the Jensen wake model, under full shielding conditions, the wake loss of wind turbine j is: When the fans have the same height: When the fan height is different: Where: Cr is the thrust coefficient of the wind turbine; k is the wake diffusion coefficient; X is the distance between the two wind turbines in the wind direction; h is the wheel height; ΔZ is the height difference between the two wind turbines |z i -z j |; In a wind farm, each wind turbine will be affected by the wake of multiple wind turbines to varying degrees under different wind direction conditions. Assuming that kinetic energy loss and wake loss are conserved, the wake effect on the j-th wind turbine can be calculated using the following formula: Where v ij is the speed of wind turbine j when it is completely blocked by the wake of turbine i; Step 3-2, when j is the upstream wind turbine and i is the downstream wind turbine; The influence of the wake of wind turbine i on wind turbine i is: d i =b ji ×d ji (6) Where: d ji is the wake loss suffered by wind turbine i when it is completely blocked by the wake of wind turbine j; β ji ＝A ji / (πr 2 ) (7) When the fans have the same height: When the fan height is different: In an actual wind farm, each wind turbine will be affected by the wake of multiple wind turbines to varying degrees under different wind direction conditions. Assuming that kinetic energy loss and wake loss are conserved, the wake effect on the i-th wind turbine is calculated using the following formula: Where v ji is the speed when wind turbine i is completely blocked by the wake of wind turbine j.

2. A wake model suitable for complex mountainous areas according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2-1: Based on the Lissaman wake model, assume that the wind speed changes exponentially with height. In the absence of a wake, the upstream wind turbine is i and the downstream wind turbine is j. The wind speed of wind turbine i is: The wind speed of wind turbine j is: In the formula is the wind shear index; v0 is the incident wind speed, z0 is the incident wind altitude, z i is the altitude of the i-th wind turbine, z j is the altitude of the j-th wind turbine, h is the hub height of the wind turbine; Step 2-2: When affected by the wake, assume that the wind speed reduction coefficient of wind turbine i is d i , the wind speed reduction coefficient of wind turbine j is d j ; The actual wind speed of wind turbine i and wind turbine j is: v′ i =v i (1-d i ) (13) v′ j =v j (1-d j ) (14) 。 3. A wake model suitable for complex mountainous areas according to claim 2, characterized in that: described It can be calculated based on wind measurement data at different heights. The formula is as follows: 。 4. The wake model suitable for complex mountainous areas according to claim 1, characterized in that: In step 3: In mountainous conditions, the incident wind will be affected by the topographic wind effect. Under the influence of the hillside, the wind flow will be subject to the upward effect and the angle will change in the vertical direction. The angle between the vertical direction and the horizontal direction is θ. Where: is the radius of the circle after the wake diffusion, b is the wake diffusion coefficient;

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