﻿ 基于实测数据的阿克苏光伏电站相关性分析

# 基于实测数据的阿克苏光伏电站相关性分析Relevance Analysis of Aksu Photovoltaic Power Station Based on Measured Data

Abstract: Uncertainty, intermittence and fluctuation of photovoltaic power generation will cause photovoltaic power generation to abandon light, and mastering its characteristics is an important basis for improving absorption. In this paper, the correlation of photovoltaic power plants is analyzed based on measured data. Firstly, the calculation method of the correlation between the output of the same photovoltaic power station at different time periods and the output of the same photovoltaic power station at different time periods is given. Secondly, the influence of cloud factor and geographic location on the output correlation of photovoltaic power station is analyzed theoretically. Finally, taking Aksu photovoltaic power station in Xinjiang as an example, the influence of cloud factor and geographic location on the output correlation of the same photovoltaic power station and the output correlation of different photovoltaic power stations are illustrated by the measured data.

1. 引言

2. 光伏电站出力相关性的计算方法

2.1. 同一光伏电站不同时段出力

(1)

(2)

${\rho }_{s}=r\left({P}^{\alpha },{P}^{\beta }\right)=\frac{\underset{i=1}{\overset{n}{\sum }}\left({P}_{i}^{\alpha }-\stackrel{¯}{{P}^{\alpha }}\right)\left({P}_{i}^{\beta }-\stackrel{¯}{{P}^{\beta }}\right)}{\sqrt{\underset{i=1}{\overset{n}{\sum }}{\left({P}_{i}^{\alpha }-\stackrel{¯}{{P}^{\alpha }}\right)}^{2}\underset{i=1}{\overset{n}{\sum }}{\left({P}_{i}^{\beta }-\stackrel{¯}{{P}^{\beta }}\right)}^{2}}}$ (3)

2.2. 同一时段不同光伏电站出力

${R}_{T}={\left[{\rho }_{T}\right]}_{M×M}$ (4)

${\rho }_{T}=r\left({P}_{T}^{f},{P}^{g}\right)=\frac{\underset{i=1}{\overset{n}{\sum }}\left({P}_{i+T}^{f}-\stackrel{¯}{{p}^{f}}\right)\left({P}_{i}^{g}-\stackrel{¯}{{P}^{g}}\right)}{\sqrt{\underset{i=1}{\overset{n}{\sum }}{\left({P}_{i+T}^{f}-\stackrel{¯}{{p}^{f}}\right)}^{2}\underset{i=1}{\overset{n}{\sum }}{\left({P}_{i}^{g}-\stackrel{¯}{{P}^{g}}\right)}^{2}}}$ (5)

3. 光伏电站出力相关性的影响因素理论分析

3.1. 云量因子

$x=\left[0,\cdots ,0,{\gamma }_{1}{x}_{1},{\gamma }_{2}{x}_{2},{\gamma }_{3}{x}_{3},\cdots ,{\gamma }_{n-2}{x}_{n-2},{\gamma }_{n-1}{x}_{n-1},{\gamma }_{n}{x}_{n},0,\cdots ,0\right]$ (6)

(7)

${y}^{\prime }=\left[0,\cdots ,0,{\beta }_{1}{{y}^{\prime }}_{1},{\beta }_{2}{{y}^{\prime }}_{2},{\beta }_{3}{{y}^{\prime }}_{3},\cdots ,{\beta }_{n-2}{{y}^{\prime }}_{n-2},{\beta }_{n-1}{{y}^{\prime }}_{n-1},{\beta }_{n}{{y}^{\prime }}_{n},0,\cdots ,0\right]$ (8)

$\rho \left(x,y\right)=\frac{\left(N-n\right)\stackrel{¯}{x}\cdot \stackrel{¯}{y}+\underset{i=1}{\overset{n}{\sum }}\left({\gamma }_{i}{x}_{i}-\stackrel{¯}{x}\right)\left({\alpha }_{i}{y}_{i}-\stackrel{¯}{y}\right)}{\sqrt{\left(\left(N-n\right){\left(0-\stackrel{¯}{x}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({\gamma }_{i}{x}_{i}-\stackrel{¯}{x}\right)}^{2}\right)\cdot \left(\left(N-n\right){\left(0-\stackrel{¯}{y}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({\alpha }_{i}{y}_{i}-\stackrel{¯}{y}\right)}^{2}\right)}}$ (9)

$\rho \left(x,{y}^{\prime }\right)=\frac{\left(N-n\right)\stackrel{¯}{x}\cdot {\stackrel{¯}{y}}^{\prime }+\underset{i=1}{\overset{n}{\sum }}\left({\gamma }_{i}{x}_{i}-\stackrel{¯}{x}\right)\left({\beta }_{i}{{y}^{\prime }}_{i}-{\stackrel{¯}{y}}^{\prime }\right)}{\sqrt{\left(\left(N-n\right){\left(0-\stackrel{¯}{x}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({\gamma }_{i}{x}_{i}-\stackrel{¯}{x}\right)}^{2}\right)\cdot \left(\left(N-n\right){\left(0-{\stackrel{¯}{y}}^{\prime }\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({\beta }_{i}{{y}^{\prime }}_{i}-{\stackrel{¯}{y}}^{\prime }\right)}^{2}\right)}}$ (10)

3.2. 地理位置

$x=\left[0,\cdots ,0,{x}_{1},{x}_{2},{x}_{3},\cdots ,{x}_{n-2},{x}_{n-1},{x}_{n},0,0,\cdots ,0\right]$ (11)

$y=\left[0,\cdots ,0,0,{y}_{1},{y}_{2},\cdots ,{y}_{n-1},{y}_{n},0,0,\cdots ,0\right]$ (12)

${y}^{\prime }=\left[0,\cdots ,0,0,0,{{y}^{\prime }}_{1},\cdots ,{{y}^{\prime }}_{n},0,0,\cdots ,0\right]$ (13)

$\rho \left(x,y\right)=\frac{\begin{array}{l}\text{}\left(N-n-2\right)\stackrel{¯}{x}\cdot \stackrel{¯}{y}+\left({x}_{1}-\stackrel{¯}{x}\right)\left(0-\stackrel{¯}{y}\right)+\left({x}_{2}-\stackrel{¯}{x}\right)\left({y}_{1}-\stackrel{¯}{y}\right)\\ +\underset{i=3}{\overset{n}{\sum }}\left({x}_{i}-\stackrel{¯}{x}\right)\left({y}_{i-1}-\stackrel{¯}{y}\right)\text{}+\left(0-\stackrel{¯}{x}\right)\left({y}_{n}-\stackrel{¯}{y}\right)+\left(0-\stackrel{¯}{x}\right)\left(0-\stackrel{¯}{y}\right)\end{array}}{\sqrt{\left(\left(N-n\right){\left(0-\stackrel{¯}{x}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({x}_{i}-\stackrel{¯}{x}\right)}^{2}\right)\cdot \left(\left(N-n\right){\left(0-\stackrel{¯}{y}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({y}_{i}-\stackrel{¯}{y}\right)}^{2}\right)}}$ (14)

$\rho \left(x,{y}^{\prime }\right)=\frac{\begin{array}{l}\text{}\left(N-n-2\right)\stackrel{¯}{x}\cdot {\stackrel{¯}{y}}^{\prime }+\left({x}_{1}-\stackrel{¯}{x}\right)\left(0-{\stackrel{¯}{y}}^{\prime }\right)+\left({x}_{2}-\stackrel{¯}{x}\right)\left(0-{\stackrel{¯}{y}}^{\prime }\right)\\ +\underset{i=3}{\overset{n}{\sum }}\left({x}_{i}-\stackrel{¯}{x}\right)\left({{y}^{\prime }}_{i-2}-{\stackrel{¯}{y}}^{\prime }\right)\text{}+\left(0-\stackrel{¯}{x}\right)\left({y}_{n-1}-{\stackrel{¯}{y}}^{\prime }\right)+\left(0-\stackrel{¯}{x}\right)\left({y}_{n}-{\stackrel{¯}{y}}^{\prime }\right)\end{array}}{\sqrt{\left(\left(N-n\right){\left(0-\stackrel{¯}{x}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({x}_{i}-\stackrel{¯}{x}\right)}^{2}\right)\cdot \left(\left(N-n\right){\left(0-{\stackrel{¯}{y}}^{\prime }\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({y}_{i}-{\stackrel{¯}{y}}^{\prime }\right)}^{2}\right)}}$ (15)

$\Delta \rho =\rho \left(x,y\right)-\rho \left(x,{y}^{\prime }\right)=\frac{{x}_{2}{y}_{1}+\left({y}_{n-1}-{y}_{1}\right)\stackrel{¯}{x}}{\sqrt{\left(\left(N-n\right){\left(0-\stackrel{¯}{x}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({x}_{i}-\stackrel{¯}{x}\right)}^{2}\right)\cdot \left(\left(N-n\right){\left(0-\stackrel{¯}{y}\right)}^{2}+\underset{i=1}{\overset{n}{\sum }}{\left({y}_{i}-\stackrel{¯}{y}\right)}^{2}\right)}}$ (16)

4. 实测数据光伏电站出力相关性分析

Table 1. Basic information of photovoltaic power station

4.1. 云量因子对相关性的影响

Table 2. Cloudiness

Figure 1. Output curve on sunny day

Figure 2. Output curve in cloudy day

Figure 3. Output curve in overcast day

Table 3. Coefficient of correlation under different cloud cover

Table 4. Correlation coefficient statistics

4.2. 地理位置对相关性的影响

Figure 4. Output curves of five power plants on sunny day

Figure 5. Output curves of five power plants on cloudy day

Figure 6. Output curves of five power plants on overcast day

Table 5. Coefficient of correlation and delay of geographical location considering delay

Figure 7. Delay characteristics of sunny day

Figure 8. Delay characteristics of cloudy day

Figure 9. Delay characteristics of overcast day

5. 结论

1) 晴天与晴天的相关系数的最小值大于除了晴天与多云天组合之外的任意组合的最大值，表明同一光伏电站出力相关性最强，原因在于两者的云量因子接近且干扰因素较小。

2) 晴天和多云天情况下，参考电站的出力序列的起始点和终止点晚于比较电站，比较电站的出力序列只有经过延时，不同地理位置的光伏电站出力相关性才能达到最强。

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