﻿ 通用的定日镜准确方位–俯仰跟踪公式及其应用研究 Study on the General Accurate Azimuth-Elevation Tracking Angle Formula for Heliostat and Its Applications

Advances in Energy and Power Engineering
Vol.03 No.05(2015), Article ID:16219,16 pages
10.12677/AEPE.2015.35019

Study on the General Accurate Azimuth-Elevation Tracking Angle Formula for Heliostat and Its Applications

Minghuan Guo, Zhifeng Wang

Key Laboratory of Solar Thermal Energy and Photovoltaic System of Chinese Academy of Sciences, IEE-CAS, Beijing

Received: Sep. 30th, 2015; accepted: Oct. 23rd, 2015; published: Oct. 26th, 2015

ABSTRACT

With respect to the widely used azimuth-elevation dual axis tracking heliostats, this paper gives the accurate azimuth-elevation tracking angle formula for a heliostat with a mirror-pivot offset and other six typical geometric error parameters. A nonlinear least-squares mathematical model is established to solve the six typical angular tracking parameters of the azimuth-elevation tracking heliostat based on experimental tracking data, and also gives the two practical numerical solution algorithms. We specially designed a heliostat model and with the help of optical test platform of 3D coordinate measuring machine conducted the indoor laser beam azimuth-elevation tracking experiments. The experimental results validated the general tracking angle formula and the method for estimating the six typical angle error parameters of an azimuth-elevation tracking heliostat. This general accurate azimuth-elevation tracking angle formula can effectively compensate the heliostat pedestal tilt, the initial angle biases of the two rotational axes and the non orthogonal angle error of the two axes and so on. This tracking angle formula has been successfully applied to the 100 heliostats in Badaling 1 MW solar thermal tower power plant (DAHAN solar power plant) in Beijing, China.

Keywords:Heliostat, Azimuth-Elevation Tracking, Tracking Angle Formula

1. 引言

DAHAN电站的定日镜场由100面单台反射面积为100 的定日镜组成，每台定日镜由64面正方形单元镜，呈8行8列排布而成，如图2所示。定日镜采用的是方位-俯仰跟踪方式。

Figure 1. Four typical heliostat dual-axis tracking modes: (1) spinning-elevation or target-oriented, (2) azimuth-elevation, (3) pitch-roll, (4) polar

(a) (b)

Figure 2. DAHAN heliostat: (a) Heliostat photo; (b) Sketch of heliostat structure

2. 镜面偏心定日镜镜面中心的准确法向

2.1. 镜面偏心定日镜的标准自旋俯仰跟踪公式

(a) (b)

Figure 3. Geometry of the standard spinning-elevation tracking heliostat with a mirror-pivot offset: (a) Geometry of spinning-elevation tracking; (b) Angular relationships of heliostat tracking and the residual tracking error in the tracking plane II

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(2)

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, (当时，) (7)

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2.2. 镜面中心法向的精度

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2.3. 镜面中心法向的鲁棒表达式

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3. 镜面偏心定日镜的准确方位–俯仰跟踪公式

3.1. 基于鲁棒镜面中心法向的通用方位–俯仰跟踪公式

(a) (b)

Figure 4. Tracking error range of the standard spinning-elevation tracking formula: (a) Calibration angle of tracking elevation angle; (b) Angle of residual tracking error

Figure 5. General azimuth-elevation tracking geometry for a heliostat with a mirror-pivot offset and other angular error parameters

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3.2. 化简后的通用方位–俯仰跟踪公式

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4. 由跟踪实验数据反求定日镜的6个典型角度误差参数

4.1. 计算镜面中心的法向

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4.2. 计算镜面中心的反射光线与靶面的交点

Figure 6. Intersection geometry of the reflected mirror-surface-centre ray with the target plane for a heliostat with a mirror-pivot offset

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4.3. 建立最小二乘法数学模型

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 太阳位置角度：

 跟踪角度：

 镜面中心反射光点(镜面中心的反射光线与目标靶面的交点)的靶面坐标：

(38)

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4.4. 两个实用的非线性最小二乘问题求解算法

 阻尼Gauss-Newton方法

Step 1：置

Step 2：计算

Step 3：计算雅克比矩阵，以及

Step 4：

Step 5：用0.618黄金分割法，反复做一维搜索，确定非负步长因子，直到满足

Step 6：，并计算，如果或者，则计算结束；

Step 7：，进行Step 2。

 Hartley-Meyer算法

Step 1：置

Step 2：计算

Step 3：计算，以及

Step 4：

Step 5：

Step 6：

Step 7：

Step 8：

Step 9：如果，则

Step 10：，并计算，如果或者，则计算结束；

Step 11：，进行Step 2。

5. 定日镜模型的激光束方位–俯仰跟踪实验

6. 通用方位–俯仰跟踪公式在北京延庆DAHAN电站的成功应用

(a)(b)

Figure 7. Azimuth-elevation laser beam tracking test setup for a special designed heliostat model on a CMM platform. (a) Geometry of the heliostat model and laser, (b) Size and position of the target plane

Figure 8. The two test heliostats (#12.4 and #-9.1) in the solar field of the DAHAN solar tower power plant

(a)(b)

Figure 9. The residual tracking error curves of two test heliostats (#12.4 and #-9.1) with different sets of angular tracking parameters in a day

Study on the General Accurate Azimuth-Elevation Tracking Angle Formula for Heliostat and Its Applications[J]. 电力与能源进展, 2015, 03(05): 123-138. http://dx.doi.org/10.12677/AEPE.2015.35019

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